OTFS methods of data channel characterization and uses thereof

ABSTRACT

Fiber, cable, and wireless data channels are typically impaired by reflectors and other imperfections, producing a channel state with echoes and frequency shifts in data waveforms. Here, methods of using OTFS pilot symbol waveform bursts to automatically produce a detailed 2D model of the channel state are presented. This 2D channel state can then be used to optimize data transmission. For wireless data channels, an even more detailed 2D model of channel state can be produced by using polarization and multiple antennas in the process. Once 2D channel states are known, the system turns imperfect data channels from a liability to an advantage by using channel imperfections to boost data transmission rates. The methods can be used to improve legacy data transmission modes in multiple types of media, and are particularly useful for producing new types of robust and high capacity wireless communications using non-legacy OTFS data transmission methods.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation application of and claims thepriorities and benefits to U.S. application Ser. No. 14/583,911, “OTFSMETHODS OF DATA CHANNEL CHARACTERIZATION AND USES THEREOF”, filed Dec.29, 2014, which further claims the priorities and benefits of U.S.provisional application 62/027,231, “METHODS OF OPERATING ANDIMPLEMENTING WIRELESS OTFS COMMUNICATIONS SYSTEMS”, filed Jul. 21, 2014;application Ser. No. 14/583,911 in turn is also a continuation in partof U.S. patent application Ser. No. 14/341,820, “ORTHONORMALTIME-FREQUENCY SHIFTING AND SPECTRAL SHAPING COMMUNICATIONS METHOD”,filed Jul. 27, 2014, now U.S. Pat. No. 9,083,483; application Ser. No.14/341,820 in turn was a continuation of U.S. application Ser. No.13/117,119, “ORTHONORMAL TIME-FREQUENCY SHIFTING AND SPECTRAL SHAPINGCOMMUNICATIONS METHOD”, filed May 26, 2011, now U.S. Pat. No. 8,879,378;application Ser. No. 13/117,119 claimed the priority and benefits ofU.S. provisional patent application 61/349,619, “ORTHONORMALTIME-FREQUENCY SHIFTING AND SPECTRAL SHAPING COMMUNICATIONS METHOD”,filed May 28, 2010; application Ser. No. 14/583,911 in turn is also acontinuation in part of U.S. patent application Ser. No. 13/430,690,“SIGNAL MODULATION METHOD RESISTANT TO ECHO REFLECTIONS AND FREQUENCYOFFSETS”, filed Mar. 27, 2012, now U.S. Pat. No. 9,083,595; applicationSer. No. 13/430,690 in turn claimed the priority and benefits of USprovisional patent provisional application 61/615,884, “SIGNALMODULATION METHOD RESISTANT TO ECHO REFLECTIONS AND FREQUENCY OFFSETS”,filed Mar. 26, 2012; application Ser. No. 13/430,690 was also acontinuation in part of U.S. patent application Ser. No. 13/117,119,“ORTHONORMAL TIME-FREQUENCY SHIFTING AND SPECTRAL SHAPING COMMUNICATIONSMETHOD”, filed May 26, 2011, now U.S. Pat. No. 8,879,378; applicationSer. No. 14/583,911 in turn is also a continuation in part of U.S.patent application Ser. No. 13/927,091, filed Jun. 25, 2013, “Modulationand equalization in an orthonormal time-frequency shiftingcommunications system”, now U.S. Pat. No. 9,130,638; application Ser.No. 13/927,091 claimed the priority and benefits of U.S. provisionalpatent application 61/664,020 filed Jun. 25, 2012; the entire contentsof all of these applications are incorporated herein by reference intheir entirety.

BACKGROUND OF THE INVENTION

Field of the Invention

This invention is in the field of telecommunications, in particular inmethods to estimate and compensate for impairments in telecommunicationsdata channels.

Description of the Related Art

Prior Art on Characterizing the Channel State of Communication DataChannels

Ever since the advent of the first transatlantic cable back in back in1858, which to the disappointment of its backers, was only capable oftransmitting data at a rate of about 100 words every 16 hours, theimpact of imperfect data channels on communications speed andreliability has been apparent to the telecommunications industry.

Making a quick transition to modern times, even modern day electronicwires (e.g. CATV cable), optical fibers, and wireless (radio) methods ofdata transmission suffer from the effects of imperfect data channels.The data channels are often imperfect because they often contain varioussignal reflectors that are positioned at various physical locations inthe media (e.g. various junctions in a 1D electrical conductor such aswires, or 1D junctions in optical conductors such as optical fiber. Forwireless communications, where the media is 3D space, these reflectorscan be radio reflectors that are positioned at various locations inspace). Regardless of media type and reflector type, reflectorstypically distort signal waveforms by creating various echo reflections,frequency shifts, and the like. The net result is that what wasoriginally a clear and easy to interpret signal waveform, sent by a datachannel transmitter will, by the time it reaches the receiver, can bedegraded by the presence of various echoes and frequency shiftedversions of an original signal waveform.

Traditionally, the telecommunications industry has tended to cope withto such problems by using statistical models of these various datachannel reflectors and other impairments to create a statistical profileof how the state of a given data channel (channel state) may fluctuateon a statistical basis. Such prior art includes the work of Clarke andJakes (R. H. Clarke. A statistical theory of mobile-radio reception,Bell Syst. Tech. J., 47, 957-1000 (1968); and W. C. Jakes (ed.),Microwave Mobile Communications, Wiley, New York, 1974)) and indeed suchmethods are often referred to in the industry as Clarke-Jakes models.

These prior art models were useful, because it helped communicationsengineers conservatively design equipment that would generally be robustenough for various commercial applications. For example, if thestatistical model predicted that waveforms too close together infrequency would tend to be smeared onto each other by channel state withsome statistical probability, then the communications specificationscould designed with enough frequency separation between channels tofunction to some level of statistical probability. Similarly if thestatistical model showed that certain statistical fluctuations inchannel states would produce corresponding fluctuations in signalintensity, then the power of the transmitted waveforms, or the maximumrate of data transmission, or both could be designed to cope with thesestatistical fluctuations.

A good review of these various issues is provided by Pahlavan andLevesque, “Wireless Information Networks, Second Edition”, 2005, JohnWiley & Sons, Inc., Hoboken N.J. This book provides a good prior artreview discussing how wireless radio signals are subject to variouseffects including multi-path fading, signal-drop off with distance,Doppler shifts, and scattering off of various reflectors.

As a specific example of prior art, consider the challenge of designingequipment for mobile cellular phones (cell phones). When a moving cellphone receives a transmission from non-moving cell phone tower (basestation), although some wireless energy from the cell phone tower maytravel directly to the cell phone, much of the wireless energy from thecell phone tower transmission will typically reflect off of variousreflectors (e.g. the flat side of buildings), and these “replicas” ofthe original cell phone tower transmission will also be received by thecell phone, subject to various time delays and power loss due to thedistance between the cell phone tower, the reflector, and the cellphone.

If the cell phone is moving, reflected “replica” of the original signalwill also be Doppler shifted to a varying extent. These Doppler shiftswill vary according to the relative velocity and angle between the cellphone tower, the cell phone, and the location of the various buildings(reflectors) that are reflecting the signal.

According to prior art such as the Clarke-Jakes models, statisticalassumptions can be made regarding average distributions of thetransmitters, receivers, and various reflectors. This statistical modelcan then, for example be used to help set system parameters and safetymargins so that, to a certain level of reliability, the system stillfunction in spite of these effects. Thus prior art allowed reasonablyrobust and commercially useful systems to be produced.

Polarization Effects:

Certain types of waves, such as light waves and radio waves, canoscillate in various directions or orientations. For example, wireless(radio waves) can be linearly polarized in a single direction, such ashorizontal or vertical directions, or they can be circularly polarizedso that the direction of the field rotation can vary in a clockwise orcounterclockwise manner. For example, wireless antennas often can beconfigured to transmit linear polarized wireless waveforms.

Often, transmitted light waves and/or radio waves consist of a coherentor incoherent mixture of various types of polarized waves. Generally ifthere is an equal mix of all polarization types, then the wave isconsidered to be not polarized. Conversely if one polarization typedominates, the wave is considered to be polarized according to thedominant polarization mode.

Reflectors often do not reflect all polarized waves in exactly the sameway. Instead reflectors often absorb some polarization modes, whilereflecting other polarization modes. For example, specular reflectors(specular reflection) often only reflects one direction of polarization,which is why polarized sunglasses are often used to cut down on glare.Other types of reflectors, such as such as ground reflection of wirelesssignals, or reflection off of irregular metal objects, can end upshifting the polarization angle of the reflected waves.

MIMO Techniques

MIMO (multiple-input and multiple-output) radio methods are commonlyused for many applications including WiFi and 3G MIMO techniques. Thebasic principles behind MIMO are described in various U.S. patents suchas Roy, U.S. Pat. No. 5,515,378, Paulraj, U.S. Pat. No. 5,345,599,various papers such as Golden et. al., “Detection algorithm and initiallaboratory results using V-BLAST space-time communication architecture”ELECTRONICS LETTERS 35(1) Jan. 7, 1999.

Phased Array Techniques

Phased array antennas are used for a broad range of applications,including RADAR, radio astronomy, AM and FM broadcasting, and the like.On the transmitter side, the basic concept is to operate multiple (e.g.N) transmitters or receivers according to the principles of N-slitdiffraction. Thus for transmission, each of the N transmitters will emitthe same waveform, each offset by a different phase shift angle. Due todiffraction principles of constructive interference and destructiveinterference, depending on the phase shift angle, the sum of theresulting waveforms from the N different antennas will impartdirectionality to the resulting transmitted beam. Similarly, forreceiving, the receiver will monitor or detect the phase shifts betweenthe same waveforms as received by N different receiving antennas, thusin effect imparting directionality to the receiver antenna array aswell. Patents on phased array methods include Shimko, U.S. Pat. No.4,931,803, and others.

Review of OTFS Methods

As previously discussed, modern electronics communications, such asoptical fiber communications, electronic wire or cable basedcommunications, and wireless communications all operate by modulatingsignals and sending these signals over their respective optical fiber,wire/cable, or wireless mediums or communications channels. Here thesevarious media are often referred to as “data channels”. In the case ofoptical fiber and wire/cable, often these data channels comprise aphysical medium (e.g. the fiber or cable), often comprising at least onedimension of space and one dimension of time.

In the case of wireless communications, often these data channels willconsist of the physical medium of space (and any objects in this space)comprising three dimensions of space and one dimension of time. (Notehowever, that in the most commonly used commercial setting of groundbased wireless applications, often the third spatial dimension of heightcan be less important, and thus ground based wireless applications canoften be adequately approximated as a two dimensional medium of space(with objects) with one dimension of time.)

As previously discussed, as signals travel through a data channel, thevarious signals (e.g. waveforms), which (at least in the case ofoptical, wireless, or electric signals) often travel at or near thespeed of light, are generally subject to various types of degradation orchannel impairments. As per the previous example, echo signals canpotentially be generated in an optical fiber or wire/cable mediumwhenever a signal encounters junctions in the optical fiber orwire/cable. Echo signals can also potentially be generated when wirelesssignals bounce off of wireless reflecting surfaces, such as the sides ofbuildings, and other structures. Similarly frequency shifts can occurwhen the optical fiber or wire/cable propagating signal passes throughdifferent regions of fiber or cable with somewhat different signalpropagating properties or different ambient temperatures. For wirelesssignals, signals transmitted to or from a moving reflector, or to orfrom a moving vehicle are subject to Doppler shifts that also result infrequency shifts. Additionally, the underlying equipment (i.e.transmitters and receivers) do not always operate perfectly, and canproduce frequency shifts as well.

These echo effects and frequency shifts are unwanted, and if such shiftsbecome too large, can result in lower rates of signal transmission, aswell as higher error rates. Thus methods to reduce such echo effects andfrequency shifts are of high utility in the communications field.

In previous work, exemplified by applicant's US patent applications U.S.61/349,619, U.S. Ser. Nos. 13/430,690, and 13/927,091 as well as U.S.Pat. Nos. 8,547,988 and 8,879,378, applicant taught a novel method ofwireless signal modulation that operated by spreading data symbols overa larger range of times, frequencies, and spectral shapes (waveforms)than was previously employed by prior art methods (e.g. greater thansuch prior art methods as Time Division Multiple Access (TDMA), GlobalSystem for Mobile Communications (GSM), Code Division Multiple Access(CDMA), Frequency Division Multiple Access (FDMA), OrthogonalFrequency-Division Multiplexing (OFDM), or other methods).

Applicant's methods, previously termed “Orthonormal Time-FrequencyShifting and Spectral Shaping (OTFSSS)” in U.S. Ser. No. 13/117,119 (andsubsequently referred to by the simpler “OTFS” abbreviation in laterpatent applications such as U.S. Ser. No. 13/430,690) operated bysending data in larger “chunks” or frames than previous methods. Thatis, while a prior art CDMA or OFDM method might encode and send units orframes of “N” symbols over a communications link (e.g. data channel)over a set interval of time, applicant's OTFS methods would typically bebased on a minimum unit or frame of N² symbols, and often transmit theseN² symbols over longer periods of time.

In some OTFS modulation embodiments, each data symbol or element that istransmitted was also spread out to a much greater extent in time,frequency, and spectral shape space than was the case for prior artmethods. As a result, at the receiver end, it often took longer to startto resolve the value of any given data symbol because this symbol had tobe gradually built-up or accumulated as the full frame of N² symbols isreceived.

Thus applicant's prior work taught a wireless communication method thatused a combination of time, frequency and spectral shaping to transmitdata in convolution unit matrices (data frames) of N·N (N²) (e.g. N×N, Ntimes N) symbols. In some embodiments, either all N² data symbols arereceived over N spreading time intervals (e.g. N wireless waveformbursts), or none were (e.g. receiving N bursts was required in order toreconstruct the original data bits). In other embodiments thisrequirement was relaxed.

To determine the times, waveforms, and data symbol distribution for thetransmission process, the N² sized data frame matrix could, for example,be multiplied by a first N·N time-frequency shifting matrix, permuted,and then multiplied by a second N·N spectral shaping matrix, therebymixing each data symbol across the entire resulting N·N matrix. Thisresulting data matrix was then selected, modulated, and transmitted, ona one element per time slice basis, as a series of N OTFS symbolwaveform bursts. At the receiver, the replica matrix was reconstructedand deconvoluted, revealing a copy of the originally transmitted data.

For example, in some embodiments taught by U.S. patent application Ser.No. 13/117,119, the OTFS waveforms could be transmitted and received onone frame of data ([D]) at a time basis over a communications link,typically using processor and software driven wireless transmitters andreceivers. Thus, for example, all of the following steps were usuallydone automatically using at least one processor.

This first approach used frames of data that would typically comprise amatrix of up to N² data elements, N being greater than 1. This methodwas based on creating an orthonormal matrix set comprising a first N×Nmatrix ([U₁]) and a second N×N matrix ([U₂]). The communications linkand orthonormal matrix set were typically chosen to be capable oftransmitting at least N elements from a matrix product of the first N×Nmatrix ([U₁]), a frame of data ([D]), and the second N×N matrix ([U₂])over one time spreading interval (e.g. one burst). Here each timespreading interval could consist of at least N time slices. The methodtypically operated by forming a first matrix product of the first N×Nmatrix ([U₁]), and the frame of data ([D]), and then permuting the firstmatrix product by an invertible permutation operation P, resulting in apermuted first matrix product P([U₁][D]). The method then formed asecond matrix product of this permuted first matrix product P([U₁][D])and the second N×N_matrix ([U₂]) forming a convoluted data matrix,according to the method, this convoluted data matrix could betransmitted and received over the wireless communications link.

On the transmitter side, for each single time-spreading interval (e.g.burst time), the method operated by selecting N different elements ofthe convoluted data matrix, and over different time slices in this timespreading interval, the method used a processor and typically softwarecontrolled radio transmitters to select one element from the N differentelements of the convoluted data matrix, modulate this element, andwirelessly transmit this element so that each element occupied its owntime slice.

On the receiver side, the receiver (typically a processor controlledsoftware receiver) would receive these N different elements of theconvoluted data matrix over different time slices in the various timespreading intervals (burst times), and demodulate the N differentelements of this convoluted data matrix. These steps would be repeatedup to a total of N times, thereby reassembling a replica of theconvoluted data matrix at the receiver.

The receiver would then use the first N×N matrix ([U₁]) and the secondN×N matrix ([U₂]) to reconstruct the original frame of data ([D]) fromthe convoluted data matrix. In some embodiments of this method, anarbitrary data element of an arbitrary frame of data ([D]) could not beguaranteed to be reconstructed with full accuracy until the convoluteddata matrix had been completely recovered. In practice, the system couldalso be configured with some redundancy so that it could cope with theloss of at least a few elements from the convoluted data matrix.

U.S. patent application Ser. No. 13/117,119 and its provisionalapplication 61/359,619 also taught an alternative approach oftransmitting and receiving at least one frame of data ([D]) over awireless communications link, where again this frame of data generallycomprised a matrix of up to N² data elements (N being greater than 1).This alternative method worked by convoluting the data elements of theframe of data ([D]) so that the value of each data element, whentransmitted, would be spread over a plurality of wireless waveforms,where each individual waveform in this plurality of wireless waveformswould have a characteristic frequency, and each individual waveform inthis plurality of wireless waveforms would carry the convoluted resultsfrom a plurality of these data elements from the data frame. Accordingto the method, the transmitter automatically transmitted the convolutedresults by cyclically shifting the frequency of this plurality ofwireless waveforms over a plurality of time intervals so that the valueof each data element would be transmitted as a plurality of cyclicallyfrequency shifted wireless waveforms sent over a plurality of timeintervals, again as a series of waveform bursts. At the receiver side, areceiver would receive and use a processor to deconvolute this pluralityof cyclically frequency shifted wireless waveforms bursts sent over aplurality of times, and thus reconstruct a replica of at least oneoriginally transmitted frame of data ([D]). Here again, in someembodiments, the convolution and deconvolution schemes could be selectedso such that an arbitrary data element of an arbitrary frame of data([D]) could not be guaranteed to be reconstructed with full accuracyuntil substantially all of the plurality of cyclically frequency shiftedwireless waveforms had been transmitted and received as a plurality ofwaveform bursts. In practice, as before, system could also be configuredwith some redundancy so that it could cope with the loss of at least afew cyclically frequency shifted wireless waveforms.

In other embodiments, the methods previously disclosed in U.S. patentapplication Ser. Nos. 13/927,091; 13/927/086; 13/927,095; 13/927,089;13/927,092; 13/927,087; 13/927,088; 13/927,091; and/or provisionalapplication 61/664,020 may be used for some of the OTFS modulationmethods disclosed herein. The entire contents of U.S. patent application62/027,231, Ser. Nos. 13/927,091; 13/927/086; 13/927,095; 13/927,089;13/927,092; 13/927,087; 13/927,088; 13/927,091; and 61/664,020 areincorporated herein in their entirety.

BRIEF SUMMARY OF THE INVENTION

The invention is based, in part, on the insight that modern electronicsand modern signal processing methods now make it possible to supplantthe earlier statistical based models of channel states, such as thepreviously discussed Clarke-Jakes model, with actual knowledge of theexact state of the data channel, and this actual knowledge can then beused to achieve much higher levels of data transmission speed, faderesistance, and reliability. Indeed improvements of one or even two ormore orders of magnitude over prior art can be realized according to themethods described herein.

As previously discussed, data channels, such as fiber, cable, andwireless data channels, are typically impaired by the presence ofreflecting structures (reflectors) and other channel imperfectionsplaced at unknown locations along the data channel. These reflectingstructures end up putting the channel into an unknown channel state inwhich transmitted waveforms traveling over the channel end up producingvarious types of echoes and frequency shifts by the time the waveformshit the receiver. The sum total of these various imperfections can becalled the “channel state” of the data channel.

The invention is based, in part on the insight that prior art methods ofestimating the state of data channels, such as the earlier Clarke-Jakesmodel, tend to view the actual channel state of any given real-worlddata channel as being essentially indeterminable. Instead prior artmethods simply tried to describe statistical average data channels, andteach conservative methods of operation that will tend to be robust tostatistical fluctuations about this average model. The cost of thisprior art approach is that on the one hand, when the actual channelstate is better than the statistical average, then the statistical datachannel approach artificially limits the rate that data is sent to alevel far lower than the data channel could actually support.Alternatively, when the actual channel state is significantly worse thanthe statistical average, then instead of gracefully adapting to the poorchannel state, prior art methods will instead experience apparentlyrandom signal fading events, and operate unreliably.

The invention is based, in part, on the insight that OTFS methods,previously used to produce a more generally robust type ofcommunications over a broad range of channel states, can also be usedfor a different purpose—producing highly accurate real-time (or nearreal-time) models of data channel states. Once such highly accuratereal-time or near real-time models of the channel state are available,then processor equipped transmitters and receivers can use thisinformation to automatically adjust their modes of data transmission andreception to continually adjust for the real-world channel state of thedata channel. This helps insure that the data channel can always beoperated at a much higher rate (often near the physical limits for thatparticular data channel and channel state), and at the same time operatemore deterministically because the system can automatically compensatefor various channel impairments.

In this disclosure, methods of using OTFS pilot symbol waveform burststo automatically produce at least a detailed 2 dimensional model of thechannel state are presented.

This method is based, in part, on the insight that although the actualchannel state of a real world data channel may be very complex, thepractice of following prior art, which teaches simply giving up andresorting instead to statistical models, can be abandoned. Insteadgreatly superior results can be obtained by using OTFS type pilot signalmethods that, often in real time, operate to map the complexities of theactual channel state into at least a simplified 2 dimensionalrepresentation of the channel state. Although this 2 dimensionalrepresentation of the channel state (here called the 2D channel state)is of course still just an approximation of the “real” channel state, itcan be very useful because this 2D channel state can then beautomatically used by the system to continually optimize datatransmission.

As will be discussed, the invention's use of OTFS pilot signals toproduce 2D channel state information can be broadly used in many aspectsof the telecommunications industry. Once the 2D channel state of even alegacy data channel transmitting legacy signals is understood, this 2Dchannel state can be automatically used by even legacy transmitters andreceivers to improve operation. Indeed, as an extreme example, if a timemachine was available, the invention's OTFS pilot signal methodsdescribed herein could even have been used to produce improved waveformsby which to transmit and receive Morse code on the original 1858transatlantic cable.

Although the methods described herein can thus be usefully employed withoptical fiber media, conducting wire media, using various types oflegacy signal transmission methods, in other embodiments, the 2D channelstate determination (acquisition) methods described herein are extremelyuseful for wireless applications.

For wireless data channels, an even more detailed 2D model of channelstate can be produced by using polarization and multiple antennas in thepilot signal process. Once the 2D channel states are known, the methodsdescribed herein can paradoxically and non-intuitively turn imperfectdata channels from a liability to an advantage, by automatically usingchannel imperfections (exposed and characterized by the 2D channelstate) to further boost data transmission rates.

Thus the OTFS pilot signal methods and 2D channel state acquisitionmethods described herein can be used to improve legacy data transmissionmodes in multiple types of media, and are particularly useful forproducing new types of robust and high capacity wireless communicationsusing non-legacy OTFS data transmission methods.

Briefly, and as an oversimplification that is not intended to belimiting, these methods operate by using OTFS pilot signal methods toacquire the 2D channel state of an impaired data channel. This can bedone by sending OTFS encoded pilot regions that are chosen to allow theimpact of the impaired data channel on the pilot symbol waveforms to beboth detectable and quantifiable. These OTFS pilot symbols are typicallytransmitted as a series of OTFS pilot waveform bursts, often spaced bytime and frequency according to an OTFS time-frequency grid. These pilotsymbols, although often described as a plurality of pilot symbols) caninclude as little as at least one actually transmitted pilot symbol,along with other zero (empty spaces) or baseline pilot symbols alongother OTFS time-frequency grid coordinates.

The receiver will typically be configured to receive channel convolutedOTFS pilot bursts according to a receiver bin structure thatcharacterizes the received OTFS pilot bursts according to frequency andtime of arrival. Typically the resolution of the receiver bin structurewill be finer (e.g. frequency and time divisions will be smaller, so asto produce higher resolution) than the resolution of the transmitterOTFS time-frequency grid so that relatively small shifts in frequencyand time of arrival can be analyzed. The pilot symbols, transmitter OTFStime frequency grid, and the receiver bin structure can be chosen so asto enable the method to detect at least some 2D channel state effectsfor that particular 2D channel state.

The receiver can then analyze the channel convoluted OTFS pilot bursts,as received according to the receiver bin structure, and determine atleast one 2D impulse response to describe how the impaired data channeldistorted the OTFS pilot bursts, and in particular how the impaired datachannel may have projected an OTFS pilot bursts from its normallyexpected (absent channel state effects) receiver bin coordinates intoother receiver bin coordinates that correspond to time delayed orfrequency shifted versions of the original OTFS pilot bursts. Herevarious 2D transformation methods, such as Z-transform methods, matrixmethods, and other transformation methods may be used. In someembodiments, data symbols may be also transmitted along with the pilotsignals. Here often the inverse of the transform that describes how theOTFS pilot burst was distorted by the data channel, or projections ofthis transform, will also suffice to clean up channel caused distortionin the data symbols as well.

As will be described, these methods can be still further enhanced by ineffect adding extra dimensions to the basic 2D channel state acquisitionmethods described herein. The extra dimension of polarization can beused to help further discriminate between different types of reflectors.The extra dimension antenna spatial separation (often in conjunctionwith monitoring waveform phase or waveform directionality) can also beused to provide more accurate 2D channel state information because thesemethods can further distinguish between various combinations of multiplespatially separated transmitting antennas, receiving antennas, andreflectors in space.

It often is unfeasible, if only prior art methods are used, to transmitmultiple streams of data (using a transmitter with multiple antennas, toa receiver with multiple antennas) using the same time, frequency, andwaveform basis shape. This is because prior art receivers are oftenunable to distinguish between these multiple streams. An additionalproblem is that prior art, which tends to assume that data channels areeither perfect or impossible to characterize by other than statisticalmethods, teaches that multiple streams can become hopelessly convolutedas they travel through the data channel, not unlike an unbreakable code,and be hopelessly jumbled by the time they reach the receiver.

However by using at least the more sophisticated versions of the 2Dchannel state acquisition methods described here, the transmitter andreceiver can utilize their superior knowledge about the 2D channel stateto take advantage of reflectors and other channel imperfections to helpseparate out the data coming from the different streams. The net effectis a bit paradoxical, in that by using these methods, an “imperfect”data channel, cluttered with various reflectors, some of which may bemoving, may actually support a substantially higher rate of datatransmission than a perfect data channel that has no reflectors and noclutter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A shows a simplified model of a wireless data channel connecting asingle transmitter and a single receiver. This simplified model has onlyone signal reflector.

FIG. 1B shows how the invention's OTFS transmitters and OTFS receiverscan use transmitter and receiver processors, along with associatedmemory, to transmit OTFS pilot and data symbols (using their associatedOTFS waveforms, times, and frequencies) according to the transmitter'sOTFS time-frequency grid, and receive OTFS symbols (using theirassociated OTFS waveforms, times, and frequencies) according to thereceiver's corresponding OTFS time-frequency bin structure. FIG. 1B alsoshows how direct OTFS pilot bursts (e.g. bursts traveling directly fromthe transmitter to the receiver without any reflections) are received atthe receiver.

FIG. 1C shows how the replica OTFS waveform bursts (e.g. bursts thatbounce off of reflectors, such as the moving reflector shown here), arereceived by the receiver according to the receiver bin structure. Hereall OTFS waveform bursts are displaced both in time (due to the distancetraveled) and frequency (due to Doppler effects).

FIG. 1D shows how the channel-convoluted OTFS waveform bursts (sum ofthe direct bursts and the replica bursts) are received by the receiveraccording to the receiver bin structure.

FIG. 2A shows how polarized OTFS pilot symbol waveform bursts can beused to further distinguish between different types of reflectors in theimpaired data channel.

FIG. 2B shows how the transmitter from FIG. 2A can transmit differenttime, frequency, and OTFS waveform synchronized streams of data from itspolarized horizontal and vertical antennas.

FIG. 2C is essentially the same as FIG. 2B, except that here thereceiver reception on the receiver's horizontal polarized antenna OTFStime-frequency bin structure is shown.

FIG. 3A shows how the system may also use MIMO (spatially separatedtransmitting and receiving antennas) and OTFS pilot symbol and datasymbol waveform bursts to both further characterize the 2D channel stateof the data channel, and also send multiple streams of datasimultaneously.

FIG. 3B shows how the MIMO transmitter from FIG. 3A can transmitdifferent, but time, frequency, and OTFS waveform synchronized, streamsof data from its spatially separated right and left antennas, and howthese are received by one of the MIMO receiver's spatially separatedantennas and corresponding bin arrangement.

FIG. 3C is essentially a repeat of FIG. 3B, except that here the signalsreceived by the MIMO receiver's other spatially separated antenna, andcorresponding bin arrangement, is shown.

FIG. 4 shows an example of how after the MIMO receiver receives the twotransmitted streams according to the OTFS bin structure on its right andleft hand antennas. The MIMO receiver processor can use the known pilotsymbols to compute the 2D channel state of the impaired data channel,and then use this to help deconvolute the OTFS data symbols as well.

FIG. 5 shows an embodiment where the OTFS pilot symbols and OTFD datasymbols are again on the same OTFS time-frequency transmitter OTFS grid,but here the OTFS pilot symbol region is embedded within the region ofthe grid otherwise used to transmit OTFD data symbols.

FIG. 6 shows an example of an OTFS transmitter using a processor (seeFIG. 1B) to transmit a series of N consecutive OTFS waveform bursts.

FIG. 7 shows an example of an OTFS receiver. As previously discussed,this receiver will normally be controlled by a receiver processor (seeFIG. 1B) and associated memory so that the receiver can simultaneouslytrack incoming OTFS waveforms at a plurality of times and frequenciesaccording to the previously described OTFS receiver bin structure.

DETAILED DESCRIPTION OF THE INVENTION

As previously discussed, the invention is based in part on the insightthat in contrast to prior art methods such as the earlier Clarke-Jakesmodel, that tended to view variations in signal strength (e.g.occasional signal fading, how long a signal remains coherent, how largea range of signal frequency ranges can be expected to be coherent) assomething that can only be handled by statistical methods, superiorresults can be obtained if the underlying structure of a data channel(communications channel) is exposed, and the various causes of signaldistortion (e.g. various reflections, frequency shifts, other shifts andthe like) are instead sorted out or “solved for”.

The main focus of this disclosure will be on wireless data channels thattransmit data (often using radio signals of various frequencies up intothe microwave frequencies and beyond) though three dimensions of space(often on earth, where the “space” may be filled with air and even othernatural airborne objects such as clouds, raindrops, hail and the like)and one dimension of time. However many of the concepts disclosed hereincan also be used for other data channels operating in other media (e.g.water, conductive metals, transparent solids, and the like). Thus use ofwireless examples is not intended to be limiting.

The invention makes use of modern electronic components, such asprocessors (e.g. microprocessors, which can even be commonly usedprocessors such as the popular Intel x86 series of processors), anddigital signal processors; and often will employ modern softwareconfigured wireless transmitters and receivers which can, for example,be implemented by various field programmable gate arrays (FPGA). Herethe methods of Harris, “Digital Receivers and Transmitters UsingPolyphase Filter Banks for Wireless Communications”, IEEE transactionsvolume 51 (4), April 2003, pages 1395-1412. Application specificintegrated circuits (ASICs) and other types of devices and methods mayalso be used.

One unique aspect of the invention is that it often transmits its pilotsymbols and data symbols as well, in the form of orthogonal time shiftedand frequency shifted wireless waveform bursts, often referred to inthis specification as OTFS pilot and data symbols and OTFS pilot anddata waveform bursts. These OTFS waveform bursts can be implemented byvarious methods, such as those previously disclosed in parentapplications U.S. 61/349,619, U.S. Ser. Nos. 13/430,690, 13/927,091 aswell as U.S. Pat. Nos. 8,547,988 and 8,879,378; all of which areincorporated herein by reference in their entirety. Although theseearlier disclosures thus contain a more detailed discussion of variousaspects of OTFS waveform technology, as well as a more detaileddiscussion as to various methods to implement OTFS symbols and dataframes, some important aspects from these disclosures will be reiteratedherein.

At least as far as transmitting data is concerned, OTFS methods work byessentially spreading out each transmitted data bit throughout aplurality of orthogonal time shifted and frequency shifted wirelesswaveform bursts so that essentially every data bit ends up travelingfrom the destination to the receiver through multiple mutuallyorthogonal wireless waveform data bursts, all based on permutations ofthe same basis waveform, distributed over a given time and frequencyrange. For efficiencies sake, a large number of data symbols (eachpotentially comprising multiple bits of data) are handledsimultaneously. Typically the OTFS matrix math (usually handled by thetransmitter processor) will repackage these data symbols into aplurality of OTFS data symbols, each OTFS data symbol in essencecontaining a portion of each data bit being transmitted). These OTFSdata symbols are used to control the modulation of each different OTFSwaveform burst, and the data is transmitted in the form of OTFS symbolmodulated OTFS waveform bursts. With regards to receiving data, thereceiver essentially has to wait to receive an entire batch (data frame)of OTFS symbols before it can begin the process of using matrix math toin essence use the received OTFS symbols to solve for the originallytransmitted data bits. Note however that OTFS pilot symbols are not usedto transmit data, and thus need not be subject to these limitations.

Thus in contrast to legacy communications methods, where some bits maybe subject to fading, and other bits will get through OK, with OTFSmethods, because each data bit travels from the transmitter to thereceiver by multiple different waveforms, all data bits, at least withina group of similarly treated data bits (often termed a data frame) willend up experiencing the same channel conditions.

To briefly summarize some aspects of these earlier disclosures, in someembodiments, data symbols intended for transmission as OTFS symbols may,on the transmitter side, be distributed, usually automatically using atleast one processor and appropriate software, over various symbolmatrices or “data frames”. These may be N·N matrices, or even N·Mmatrices (where M is different from N). These symbol matrices or dataframes are then used as input to control the modulation of the system'swireless transmitter(s). Specifically the data symbols intended fortransmission may be used to weigh or modulate a family of cyclicallytime shifted and cyclically frequency shifted waveforms.

This can be done by, for example, at the transmitter using the datasymbols to control the operation of a bank of wireless signal modulators(e.g. QAM modulators, which may be implemented using the previouslydiscussed methods of Harris or other methods). The resulting output can,for example, result in a plurality of bursts of QAM modulated waveforms,over a plurality of frequencies and time shifts, which can later be usedby the receiver to help identify the structure of the data channel (e.g.positions and velocities of various reflectors).

Although these waveforms may then be distorted during transmission,their basic cyclic time and frequency repeating structure can be used bythe system's receivers, along with appropriate receiver baseddeconvolution methods, to correct for these distortions by utilizing therepeating patterns to determine the type of deconvolution needed.

An important distinction between OTFS pilot symbols, and OTFS datasymbols, is that the OTFS pilot symbols are typically not used totransmit any data. Rather they are used for purposes of analyzing thestructure of the data channel (e.g. acquire the 2D channel state). Thusthe main requirement for an OTFS pilot symbol is that the receiver beable to recognize it as being a special, non-data carrying, OTFSwaveform burst that is going to be distorted by the data channel in thesame way that the OTFS data carrying waveform bursts are going to bedistorted. Thus the for OTFS pilot symbols complex matrix math used toencode data bits into the OTFS data symbols, and then to decode the databits from the OTFS data symbols, is not needed.

In some embodiments, where it is desired only to characterize the 2Dstate of the data channel, the OTFS pilot symbols can be used withouttransmitting any OTFS data symbols. This 2D channel state information inturn can be used to help facilitate transmission of data according tovarious legacy modes, from Morse code on wires (as an extreme legacyexample) to various wireless data transmission modes such as CDMA, 3G,4G, and the like.

When used in conjunction with OTFS data symbols, there is no absoluterequirement that the OTFS pilot symbols operate using the same basisOTFS waveform as the OTFS data symbols. However in a preferredembodiment, it is useful to transmit the OTFS pilot symbols and OTFSdata symbols using the same OTFS waveform bursts, so that the effect ofthe data channel on the OTFS pilot bursts tracks the effect of the datachannel on the OTFS data symbols as closely as possible.

To make it easier for the receiver to use the channel convoluted versionof the OTFS pilot bursts to determine the 2D channel structure, often itwill be useful to surround a given OTFS pilot burst with either nullsignals (e.g. neighboring regions on the transmitter OTFS time-frequencygrid where no signal is transmitted), or neighboring “background” OTFSpilot-background bursts that the receiver can easily distinguish fromthe channel shifted versions of the OTFS pilot burst. For this reason,the null or background OTFS regions surrounding any given OTFS pilotburst can be viewed as being a special type of OTFS pilot burst in theirown right. Thus the methods described herein will typically speak oftransmitting a plurality of OTFS pilot bursts, but it should beunderstood that some of these OTFS pilot bursts may be spaces or nullssurrounding at least one, positive energy, actually transmitted, OTFSpilot burst waveform.

In a preferred embodiment, the receiver should ideally know in advancehow a proper distribution of transmitted OTFS pilot bursts should bereceived at the receiver bins, at least in the case where there are nochannel convolution effects. Assuming that this a-priori pilotinformation is available, then the receiver's processor can base itssubsequent deconvolution calculations on the assumption that anynon-ideal distribution of OTFS pilot bursts on the bins is due tochannel distortion effects. This simplifies the calculations, and helpsinsure higher accuracy.

Method of Acquiring the 2D Channel State of an Impaired Data Channel:

Again, it should be stressed that the methods described herein can applygenerally across a variety of data channels, using either legacy or OTFStype data communications methods. Thus although various wirelessexamples and embodiments are provided here because such examples areeasy to visualize, these examples and embodiments are not intended to belimiting.

Thus in some embodiments, the invention may be an automated method ofacquiring a 2D channel state of an impaired data channel connecting atleast one transmitter and at least one receiver. As previouslydiscussed, and also as shown in FIG. 1, this impaired data channel willgenerally comprise at least one reflector. Each reflector will in turncomprise at least a reflector location (e.g. physical location in thedata channel), reflector frequency shift, and at least one reflectorcoefficient of reflection. As will be discussed, reflectors may alsohave additional properties as well.

FIG. 1A shows a simplified model of a wireless data channel (100), hereconnecting a single transmitter (102) and a single receiver (104). Here(for simplicity) assume that the transmitter and receiver are not movingwith respect to each other (although often they may also be moving aswell). This data channel is impaired by the presence of one movingreflector (106) moving at a defined velocity (108). Some OTFS pilotwaveform bursts (110) (112) travel directly from the transmitter to thereceiver. Other OTFS pilot bursts are replica OTFS pilot bursts thathave reflected off of the moving reflector (114 a, 114 b), and aretherefore reflector time-delayed and reflector frequency shifted. Thereceiver thus receives a combination of the direct and replica OTFSpilot bursts as channel-convoluted OTFS pilot bursts. The order ofarrival of the OTFS pilot bursts to the receiver is 1) Direct OTFS pilotburst (112) and then frequency shifted replica OTFS pilot burst (14 b).

Each transmitter will generally comprise a transmitter location (e.g.physical location in the data channel) and transmitter frequency shift,and each receiver will similarly comprising a receiver location(physical location in the data channel) and receiver frequency shift.The 2D channel state will generally comprise information pertaining tothe relative locations, frequency shifts, and reflector coefficients ofreflection of at least some of the various transmitters, receivers, andreflectors operating in the data channel.

According to the invention's methods, the method will use this at leastone transmitter, controlled by at least one transmitter processor, totransmit direct OTFS pilot (waveform) bursts. These direct OTFS pilotbursts will generally comprise a plurality of OTFS pilot symbolsP_(pt,pf) transmitted as OTFS pilot symbol waveform burstsP_(pt,pf)·W_(p)(pt, pf), over a plurality of combinations of times ptand frequencies pf. Here each of the pt and pf may be unique pilottime-frequency coordinates chosen from a two dimensional pilot OTFStime-frequency grid. All OTFS pilot symbol waveform burstsP_(pt,pf)·W_(p)(pt, pf) (or at least all transmitted at non-zero powerlevels) are mutually orthogonal waveform bursts derived from cyclicallytime and frequency shifted versions of a same OTFS pilot basis waveformW_(p).

Because these OTFS pilot symbol waveform bursts are not used to transmitdata, but rather are used to characterize (acquire) the 2D channel stateof the data channel, there is a fair amount of flexibility possible inthe choice of OTFS pilot symbol waveform bursts. However one requirementis that the plurality of OTFS pilot symbols P_(pt,pf) (transmitted asOTFS pilot symbol waveform bursts P_(pt,pf)·W_(p)(pt, pf)) shouldcomprise at least one non-null OTFS pilot symbol P_(pt,pf) that istransmitted as an OTFS pilot symbol waveform burst P_(pt,pf)·W_(p)(pt,pf). The power levels should be chosen so that this OTFS pilot symbolshould be detectable by at least one receiver. In a preferredembodiment, the OTFS pilot symbol will also be chosen so that it can beidentified by the receiver as a pilot symbol, and not be confused asbeing an OTFS data symbol.

In some embodiments, at least some of the plurality of OTFS pilotsymbols can be null pilot symbols, which instruct the transmitter to notapply any power to the underlying W_(p)(pt, pf) waveform (e.g.P_(pt,pf)·W_(p)(pt, pf)=0). These null pilot symbols are intended tocreate at least some empty pt and pf unique pilot time-frequencycoordinates on the two dimensional pilot OTFS time-frequency grid whereno waveform burst is transmitted. These empty regions make it easier forthe receiver to detect any channel convoluted OTFS pilot bursts thathave been projected by the channel onto that (what should otherwise be)empty grid location.

Alternatively, in some embodiments, at least some of the plurality ofOTFS pilot symbols can be transmitted as a series of uniform orstandardized background pilot symbols (and associated waveforms)intended to create a uniform background of pt and pf unique pilottime-frequency coordinates chosen from the two dimensional pilot OTFStime-frequency grid. Here the transmitter will transmit theP_(pt,pf)·W_(p)(pt, pf) with power. These background pilot symbols areintended to create a standardized background to again enable projectionsof channel-convoluted non-null (regular) OTFS pilot bursts onto thisuniform background to be detectable and quantifiable by the receiver(s).

Regardless of choice of pilot symbols and pilot symbol waveform bursts,the receiver will be configured to receive at least these pilot bursts(in some embodiments, the receiver will also receive OTFS data bursts,but this is not required) according to at least a two dimensional pilotOTFS time-frequency bin structure with bin sizes and bin-coordinatepositions proportional to the OTFS time-frequency grid used for pilotand data transmission. Here the resolution of the receiver bins willtypically be at least equal to, and preferably greater than, theresolution of the transmitter grid structure. The general idea is thatthe receiver bin structure should be chosen to be sensitive to datachannel caused delays and frequency shifts, and generally a finer(smaller) receiver bin structure will be more sensitive to theseeffects. Note that of course the practical constraints of receiverdesign, and also the fact that a finer (smaller) receiver bin will inessence capture fewer photons of OTFS waveform energy on a per binbasis. Thus at some point, an extremely fine bin structure will besubject to diminishing returns due to noise limitations. Thus thereceiver bins cannot be infinitely small bins in time and frequency.

FIG. 1B shows how both the OTFS transmitter (102) and OTFS receivers(104) generally use transmitter and receiver processors (102 p) (104 p),in addition to the transmitter and receiver circuitry (102 c), (104 c),along with associated memory (102 m), (104 m), to transmit OTFS symbols(using their associated OTFS waveforms, times, and frequencies) from thetransmitter OTFS grid (102 g), and receive OTFS symbols (using theirassociated OTFS waveforms, times, and frequencies) into the receiverOTFS bins (104 b).

FIG. 1B also shows how the direct OTFS pilot bursts (112) and any OTFSdata bursts are received at the receiver. Here the transmitter (102)transmits various types of OTFS waveform bursts, such as various OTFSpilot symbol waveform bursts 120) and various OTFS data symbol waveformbursts (130) spaced by various time and frequencies according totransmitter OTFS grid structure (102 g).

Here (120) represents the two dimensional pilot OTFS time-frequency gridwith OTFS pilot symbol waveform bursts P_(pt,pf)·W_(p)(pt, pf). Withregards to optional transmission of data, (130) represents the twodimensional OTFS data time frequency grid with OTFS data symbol waveformbursts D_(dt,df)·W_(d)(dt, df). Although there is no absoluterequirement that the OTFS pilot symbols and OTFS data symbols betransmitted and received according to their relative positions in thesame transmitter OTFS grid (102 g) and receiver OTFS bin (104 b)structures, often the pilot and data symbols will be transmitted andreceived according to the same grid and bin structure, and thus thismore common option is shown here.

The transmitter transmits at least one positive energy OTFS pilot symbolburst (1) (122) (in this example surrounded by a number of empty (0) orbackground spacers which may have zero energy). Other options are alsopossible, and these will be discussed later in this specification. Inthis example, the transmitter is also sending a number of OTFS datasymbol waveform bursts (130) at other time-frequency locations along thesame transmitter OTFS grid (102 g). Here the direct path (112) thatthese waveform bursts use to travel through the data channel is shown.

The receiver (102) is configured to receive the channel convoluted OTFSsymbols typically according to a receiver time-frequency bin structure(104 b) that is usually finer grained (higher resolution) than thetransmitter grid (102 g). Here using such a higher resolution receiverbin resolution (finer divisions in time and frequency) (104 b) isgenerally preferred higher resolution bins help the receiver betterresolve the 2D channel state of the data channel. As a rule of thumb, itis desirable to have each receiver bin be at least twice the resolution(e.g. occupy less than half of the time and frequency space) as thecorresponding spacing of the transmitter OTFS grids. Often still higherbin resolutions may be desirable.

In FIG. 1B, assuming that the receiver (104) and transmitter (102) arenot moving with respect to each other, the only data channel effect withregards to the direct OTFS bursts (112) is that all bursts are timedelayed according to the distance between the transmitter and receiver.(In this wireless example, assume that these time delay effects speed oflight related.) If the transmitter (102) and receiver (104) had beenmoving with respect to each other, then all bursts would have been alsodisplaced along the receiver OTFS bin frequency axis due to Dopplereffects.

In a preferred embodiment, where the transmitter (102) (specifically thetransmitter processor 102 p and transmitter memory 102 m) will selectthe OTFS pilot symbol waveform bursts (120) according to a scheme thatis known by the receiver (e.g. the receiver processor 104 p and receivermemory 104 m), the task of any receiver processor(s) (104 p) and memory(104 m) to determine the 2D channel impulse responses and the 2D channelstate is greatly simplified. Note that in the simplified example shownin FIG. 1B, the transmitter (102) has only one antenna, and the receiver(104) has only one antenna. As will be discussed later in thisspecification, this is not always the case.

In some embodiments, the transmitter circuitry (102 c) may be configuredto transmit multiple grids (102 g) of OTFS symbols using multipletransmitter antennas, sometimes at different polarizations, andsometimes also adjusting the direction and/or phase of the waveformsacross multiple antennas. These embodiments will also be discussed infurther depth shortly.

Similarly in some embodiments, the receiver circuitry (104 c) may beconfigured to receive signals using multiple receiver antennas. Thereceiver circuitry may also be configured (in conjunction with thesemultiple receiver antennas to detect the polarization, direction orphase of the incoming waveforms as well. Thus in these more complexschemes, the receiver may also be simultaneously receiving more than onebin (104 b) of OTFS symbols at the same time as well. Note further thatbecause, according to OTFS methods, OTFS symbols are transmitted usingmutually orthogonal waveforms, in some embodiments, it may be useful toconfigure the receiver circuitry (104 c) to be able to detect datachannel caused projection of a first OTFS symbol transmitted using afirst OTFS waveform onto a second OTFS symbol transmitted according to asecond OTFS waveform because the two waveforms are mutually orthogonalto each other.

Note that in FIG. 1B, although examples of two dimensional transmitterOTFS grids (102 g) and receiver OTFS bins (104 b) are shown, thisrepresents just the simplest embodiment. In other embodiments, to bediscussed, the OTFS transmitter grid (102 g) and/or the receiver OTFSbins (104 b) can also have optional additional dimensions in addition tothe time and frequency dimensions shown in the illustration. Examples ofsuch optional additional dimensions include polarization dimensions,phase dimensions, angle of transmission or reception direction, andmixtures of the orthogonality of the received OTFS waveforms dimensions.

As can be seen in FIG. 1A, upon propagation through the impaired datachannel (100), the direct OTFS pilot bursts then travel over at leastone path. These paths can include direct OTFS pilot bursts travelingdirectly from the transmitter to the receiver (112); and replica OTFSpilot bursts. These replica OTFS pilot bursts are typically direct OTFSpilot bursts (114 a, 114 b) that have reflected off of at least onereflector (106) before reaching the receiver. As a result, what wereoriginally direct OTFS waveform bursts (112) have now been furtherreflector time-delayed (because they have had to travel a longerdistance) and also reflector frequency-shifted (assuming that thereflector may be moving) by the time these replica OTFS pilot bursts(114 b) reach the receiver (104).

As a result, by the time that the direct (112) and replica (114 b) OTFSpilot (waveform) bursts reach the receiver, constructive and destructiveinterference will occur. For example, even the direct OTFS pilot bursts(112) may be both time delayed (due to the distance between thetransmitter and receiver) and also frequency shifted (because thetransmitter and receiver may not be precisely accurate, or because thetransmitter and receiver may be moving with respect to each other, orother effects). Thus the resulting combination of any transmitterfrequency shifted and receiver frequency shifted direct OTFS pilotbursts (112), when combined with the various replica OTFS pilot (114 b)bursts, will produce channel-convoluted OTFS pilot bursts.

So in essence the data channel (100) has scrambled or convoluted theoriginal OTFS pilot bursts to an unknown extent. Here, according to theinvention's methods, however, at the receiver (104), the method will usethe receiver's bin structure (104 b) to receive these channel-convolutedOTFS pilot bursts, and the method will use at least one processor(typically the receiver processor 104 p and memory 104 m) to determine(often essentially in real time) the 2D channel state of the impaireddata channel (100) that connects the transmitter(s) and receiver(s).

FIG. 1C shows how the replica OTFS waveform bursts (114 a), bouncing offof the reflector (106) which is moving at a certain velocity (108), arereceived by the receiver (104) according to the receiver's bin structure(104 b). Here the OTFS waveform bursts (114 b) are displaced in bothtime (due to the distance traveled along 114 a and 114 b) and frequency(due to Doppler effects due to the reflector velocity 108).

FIG. 1D shows how the channel-convoluted OTFS waveform bursts (sum ofthe direct bursts 112 from FIG. 1B, and the replica bursts 114 a and 114b from FIG. 1C) are received by the receiver (104) according to thereceiver bin structure (104 b). The receiver is now receiving a morecomplex mix of signals, but the same methods used to deconvolute theOTFS pilot symbol waveform bursts (120) will also work to deconvolutethe OTFS data symbol waveform bursts as well (130). Note that in a realworld situation, there typically will be many reflectors operating, somemoving some not. Additionally there may be more than one transmitter andreceiver (some moving, some not) and also, as will be discussed, thetransmitters and receivers ma have multiple antennas. Thus in the realworld, there will be a very complex set of channel convoluted OTFSwaveform bursts at the receiver(s) (104).

In some embodiments, the 2D channel state can be represented by a matrixor other mathematical transform that describes, for the impaired datachannel, how some or all signals transmitted by the transmitter arecoupled with some or all signals from the transmitter that are receivedby the receiver.

Before going into the various details of how the processor (usuallyreceiver processor(s) 104 p) can take the raw data obtained from thereceiver bin structure (104 b), and transform this raw data into 2Dchannel state information, it is important to spend a bit more timediscussing how OTFS pilot symbols (120), the transmitter OTFStime-frequency grid (102 g), and the receiver OTFS time frequency bins(104 b) are chosen.

In general, choice of grid structure (102 b), bin structure (104 b), andOTFS pilot symbols (e.g. 120, 122) should be motivated by practicalconsiderations regarding the data channel (100), reflector spacing orpositions (106) relative to the positions of the transmitter(s) andreceiver(s), and expected data channel frequency shifts. The main goalis that the scheme (e.g. transmitter OTFS grid structure 102 g, receiverbin structure 104 b) should capture at least some of the underlyingdetails of this expected reflector spacing and expected frequencyshifts.

Thus the speeds of waveform propagation through the data channel,waveform wavelengths, and for wireless data channels, considerationssuch as likely speeds of the transmitters, receivers, and reflectors(which cause Doppler frequency shifts) are all valid considerations. Agrid or bin structure that for example, extends too narrowly(insufficiently) in frequency or too short (insufficiently) in time tocapture important details of the 2D channel structure may be suboptimumor even useless.

Similarly a grid or bin structure that is too coarse (e.g. spacing toobig) so that important details of the 2D channel structure are missed(e.g. all received signals end up in one receiver bin) will again besuboptimum or even useless.

Typically the system will make these selections prior to transmission,generally according to the underlying physics of the data channel, butalso according to any regulatory constraints or commercial constraintsas needed. Thus regulations may place limits on allowable frequencyranges and allowable transmitter powers, for example. Commercialconstraints, such as latency time considerations, may also placeconstraints on extent to which the grid extends in time as well.

More specifically, prior to transmission, the plurality of OTFS pilotsymbols P_(pt,pf), (120) transmitter two dimensional pilot OTFStime-frequency grid structure (102 g), and receiver two dimensionalpilot OTFS time-frequency bin structure (104 b) should be chosen tousefully capture details of the data channel. This choice should besuch, for example, that if, after transmission by the transmitter(s),the impaired data channel subsequently causes at least some of the OTFSpilot symbol waveform bursts P_(t1,f1)·W_(p)(t1, f1) originallytransmitted at a first time-frequency (transmitter grid) coordinate tobe projected onto different OTFS pilot symbol waveform burstsP_(t2,f2)·Wp(t2, f2) originally transmitted at a differenttime-frequency (transmitter grid) coordinate, these effects can bedetected by the receiver. Specifically the receiver bin structure andreceiver receiving circuitry should be such that when these projectionsoccur, and OTFS pilot symbol waveform bursts are projected intodifferent bins (e.g. bins with a time and frequency different from thosenominally corresponding to the original OTFS pilot symbol waveformbursts P_(t1,f1)·W_(p)(t1, f1)), at least some of these projections willbe detectable and quantifiable by the receiver(s). Here, for example,standards can be set up, and/or the transmitter and receiver software(which may also be stored in memory such as 102 m, 104 m) designed toensure that the grid structure and the bin structure are set upappropriately the data channel at hand.

Returning to the issue of how the processor (often the receiverprocessor 104 p) can take the raw data obtained from the receiver binstructure (104 b), and transform this raw data into 2D channel stateinformation—here various methods may be used. Often these will besoftware implemented methods that may be implemented using the receiverprocessor(s) (104 p) and associated memory (104 m), but other methods,such as more specific hardware methods, may also be used.

In one scheme, the 2D channel state can be at least partially determinedby using at least one 2D impulse response to mathematically describe howthe impaired data channel (100) causes at least some of the OTFS pilotsymbol waveform bursts P_(t1,f1)·W_(p)(t1, f1) transmitted at a firsttime-frequency coordinate to be projected onto either different OTFSpilot symbol waveform bursts P_(t2,f2)·Wp(t2, f2) originally transmittedat a different time-frequency coordinate, and/or and receiver bins (104b) different from those nominally corresponding to the OTFS pilot symbolwaveform bursts P_(t1,f1)·W_(p)(t1, f1).

Here, for example, the method may further use a plurality of these 2Dimpulse responses from a plurality of receiver bins to at leastpartially describe the 2D channel state as a 2D Z-transform or othertype of 2D transform. Such Z-transforms are described by Oppenheim et.al., in chapter 3 of “Discrete-Time Signal Processing, Second Edition,Prentice Hall, 1999, and elsewhere.

In this scheme, the 2D channel state can be viewed as a type of blurringfunction which in effect blurs the originally “sharp” signalstransmitted by the transmitter according to individual specificcoordinates on the transmitter OTFS grid (102 g) and smears thesesignals over multiple receiver bins (104 b), as is illustrated insimplified form by FIG. 1D. Here, once the smearing of a known signal(here the pilot signals) are characterized, then the same transformsused to deconvolute the pilot symbols should also work to deconvolutethe data symbols as well.

Although in some embodiments, as few as one OTFS pilot symbol waveformwith non-zero energy (surrounded by appropriate null or zero-energyspaces in the appropriate OTFS transmitter grid structure such as isshown in 120) may be transmitted; in other embodiments a substantialnumber of non-zero energy OTFS pilot symbol waveforms may betransmitted. Transmitting a plurality of non-zero energy OTFS pilotsymbol waveforms can have the advantage of enabling the 2D channel stateof the data channel to be established at a still higher degree ofaccuracy. However the costs of this later approach may be that theamount of OTFS data or legacy data (if any) transmitted at the same timemay be reduced. For example, if the amount of space on the transmittergrid (102 g) used to transmit OTFS pilot symbols (120) increases, thenat some point the amount of space on the transmitter grid (102 g) usedto transmit OTFS data symbols (130) will by necessity be decreasedbecause the transmitter grid (102 g) is not of infinite size in eithertime or frequency. OTFS data symbols can still be transmitted in thiscase, but according to a subsequent data carrying grid frame, which canincrease latency.

There are additional considerations as well. For example, the OTFS pilotsymbols should ideally be chosen to make the subsequent determination ofthe 2D channel state by the receiver relatively unambiguous, andpreferably also chosen to reduce the computational loads on the receiverprocessor(s) (104 p) as well. As before, typically the plurality of OTFSpilot symbols P_(pt,pf) and their OTFS grid locations will be chosenaccording to a common scheme understood by both the transmitter and thereceiver so that the receiver processor (104 p) clearly recognizes whichbin locations (104 b) represent channel convoluted pilot symbols.

Various schemes may be used here. In some embodiments, the plurality ofOTFS pilot symbols may be one or two dimensional m-sequences (or partialm-sequences) comprising binary maximal-length shift register sequences,delta values P_(i,j) surrounded by regions of P_(pt,pf) zero values.Such sequences are described by Xiang, “Using M-sequences fordetermining the impulse responses of LTI-systems” Signal Processing 28(1992), pages 139-152. Alternatively other pilot symbol schemes, such asone or two dimensional Barker codes, Costas arrays, Walsh matrixes, andthe like may also be used. Here again the criteria are that thisplurality of pilot symbols should be selected to facilitate acquisition(e.g. characterization) of the 2D channel state of the data channel. Asbefore, the receiver bin structure (104 b) should generally be chosen sothat the various receiver OTFS time-frequency bins will havetime-frequency resolutions that are equal to or more precise than thetime-frequency resolutions of the OTFS transmitter grid (102 g).

Transmitting Data:

Of course the 2D channel state of a data channel, in and of itself, isgenerally of little use unless it is then subsequently used to helpfacilitate data transmissions. The pilot methods described herein canproduce 2D channel state information that can be useful for transmittingeither legacy data (that is, data formatted according to essentially anyprior-art non-OTFS methodology), or for data transmitted by OTFS methodsas well.

Although in some embodiments, any data transmission can be timed tooccur either before or after the 2D channel state of the data channel isdetermined by the methods described herein (for example, transmitting afirst OTFS grid (102 g) frame with nothing but data symbols, followed byeither legacy data transmissions, or transmissions of a second OTFS gridframe with data symbols), in some embodiments, it will be useful totransmit data (by either legacy or OTFS methods) along with the OTFSpilot (waveform) bursts.

In this scheme, the system will generally also use the transmitter (102)and at least one processor (usually a transmitter processor 102 p) totransmit a plurality of data symbols through the impaired data channel(100). This plurality of data symbols will itself typically betransmitted as direct data bursts comprising a plurality of datacarrying waveform bursts. These direct data (waveform) bursts may betransmitted along with the direct OTFS pilot bursts to the receiver(s).These direct data bursts will also be reflected off the reflector(s)(e.g. 106), also producing replica data bursts. These replica data(waveform) bursts will, as before, comprise time-delayed and reflectorfrequency-shifted direct data bursts. When the direct and replica databursts reach the receiver(s), constructive and destructive interferencewill again occur. As before, these direct data bursts may also besubject to transmitter frequency shifting or receiver frequency shiftingcaused by imperfections in the transmitters or receivers, motion of thetransmitters and receivers, and the like). At the receiver(s), theresulting combination of any these direct data bursts (which may betransmitter frequency shifted and receiver frequency shifted), andreplica data bursts will produce channel-convoluted data bursts.

If a large amount of complex and unknown data symbols were transmitted,and absent any 2D channel state information obtained from the OTFS pilotbursts, the receiver processor might encounter great difficulty indeconvoluting these channel-convoluted data bursts. However according tothe methods described herein, the receiver can take advantage of this 2Dchannel state information, and use at least one processor (usually areceiver processor 104 p and memory 104 m) to deconvolute at least someof the various channel-convoluted data bursts. This allows the receiverto derive at least an approximation of the originally transmittedplurality of data symbols.

Alternatively or additionally, the receiver can also send commands backto the transmitter. (Here assume that the receiver has its owntransmitter, and the transmitter in turn has its own receiver). Thesecommands, which can be based on the 2D channel state obtained by thereceiver, or indeed can be a copy of some or all of the 2D channel stateobtained by the receiver, can then be used by the transmitter(s)processors (102 p) and associated memory (102 m) to precode at leastsome of the direct data bursts to pre-compensate for the impaired datachannel. Thus for example, if the impaired data channel (100) induces aparticular distortion, the transmitted signal can be adjusted with ananti-distortion factor such that by the time the precoded signal reachesthe receiver, the anti-distortion factor cancels out the distortioncaused by impaired data channel, thus resulting in a relatively cleanand undistorted signal at the receiver.

Although the methods described herein can be used to help improve theefficiency of transmitting even legacy (prior art) data according tolegacy methods (here Morse code on the original 1858 transatlantic cableis being used as an extreme example to emphasize this point), the 2Dchannel state characterization methods used herein can be most usefulwhen used in conjunction with data that is also being transmitted byOTFS methods. These OTFS data transmission methods are further describedbelow.

In a preferred embodiment, the direct data bursts will transmit at leastsome of the plurality of data symbols as direct OTFS data bursts. Thesedirect OTFS data bursts will generally comprise a plurality of OTFS datasymbols D_(dt,df) transmitted as OTFS data symbol waveform burstsD_(dt,df)·W_(d)(dt, df) over a plurality of combinations of times dt andfrequencies df. Here dt and df are unique data time-frequencycoordinates (dt, df) chosen from a two dimensional OTFS datatime-frequency grid, such as (130). Generally all of the OTFS datasymbol waveform bursts D_(dt,df)·W_(d)(dt,df) will comprise originallytransmitted OTFS data symbols D_(dt,df) transmitted by mutuallyorthogonal waveform bursts derived from cyclically time and frequencyshifted versions of a same OTFS data basis waveform W_(d). As perprevious OTFS discussions, each data bit (and data symbol which may beformed from multiple data bits) is distributed over this plurality ofOTFS data symbols D_(dt,df). These OTFS data bursts travel thorough thedata channel as direct OTFS data bursts and replica OTFS data bursts asdescribed previously. At the receiver(s), they constructively anddestructively combine, producing channel-convoluted data bursts. Herethese are called channel-convoluted OTFS data bursts.

According to this joint OTFS pilot symbol OTFS data symbol transmissionscheme, the individual data symbols in the plurality of data symbols areencoded into a plurality of OTFS data symbols D_(dt,df) at thetransmitter prior to transmission, often using the transmitterprocessor(s) (102 p) and memory (102 m). As per other OTFS datatransmission methods, the OTFS data encoding is such that the receivermust successfully receive a plurality of OTFS data symbols D_(dt,df) toprovide enough information to determine any of the individual datasymbols.

As per other OTFS data transmission schemes, the plurality of OTFS datasymbol waveform bursts D_(dt,df)·W_(d)(dt, df) are each are mutuallyorthogonal waveform bursts derived from a same OTFS data basis waveformW_(d). At the receiver, the receiver bin structure (104 b) is such thatin addition to encompassing any OTFS pilot symbols (e.g. 120), the binstructure (104 b) further encompasses the two dimensional OTFS datatime-frequency grid (e.g. 130) as well. Put in yet another way, theextent of the receiver bin structure (104 b) in time and frequency, andthe resolution of the individual receiver bins, will at least match andpreferably exceed the extent of the transmitter grid structure (102 g)in time and frequency, as well as resolution.

In some embodiments, it will be useful to ensure that the OTFS pilotsymbol waveform bursts and OTFS data symbol waveform bursts aretransmitted and received in a highly coordinated manner. To do this,here as per FIG. 1B, the OTFS data symbol waveform burstsD_(dt,df)·W_(d)(dt, df) (130) and the plurality of OTFS pilot symbolwaveform bursts P_(pt,pf)·W_(p)(pt, pf) (120) should be chosen from acommon plurality of times t and frequencies f, where each of the t andfare unique time-frequency coordinates (t, f) chosen from a common gridof two dimensional OTFS time-frequency coordinates (102 g). According tothis coordinated OTFS pilot and data transmission scheme, thetime-frequency coordinates (td, fd) for the individual OTFS data symbolwaveform bursts should preferably be further chosen as to not overlapwith the time-frequency coordinates (pt, pf) for the OTFS pilot symbolwaveform bursts. Here of course, overlapping is undesirable as it cancause confusion between the OTFS pilot symbols used to determine oracquire the 2D channel state, and OTFS data symbols used to transmitdata. Note however that there is no requirement that all possiblecoordinates on the OTFS data time-frequency grid be filled with OTFSpilot symbols and data symbols. For example, even as shown in FIG. 1B,there can be some unused grid coordinates.

Indeed in some embodiments the OTFS data time-frequency grid may only besparsely occupied with OTFS pilot symbols and data symbols. Thus ingeneral, the OTFS data OTFS data symbol waveform burstsD_(dt,df)·W_(d)(dt,df) and the plurality of OTFS pilot symbols P_(pt,pf)transmitted as OTFS pilot symbol waveform bursts P_(pt,pf)·W_(p)(pt, pf)do not need to occupy all unique time-frequency coordinates (dt, df)chosen from the two dimensional OTFS data time-frequency grid.

Note also that there is no requirement that all positive energy OTFSdata symbol waveform bursts (here the “1” (122) in FIG. 1B) or pilotsymbols be transmitted at the same energy or power level. Instead insome embodiments, the plurality of OTFS data symbol waveform burstsD_(dt,df)·W_(d)(dt,df) and the plurality of OTFS pilot symbols P_(pt,pf)transmitted as OTFS pilot symbol waveform bursts P_(pt,pf)·W_(p)(pt, pf)may be transmitted at different power levels. Here, for example, someOTFS data symbol waveform bursts or some OTFS pilot symbol waveformbursts can be sent at power levels chosen according various criteriasuch as the 2D channel state, the distance from a given transmitter to agiven receiver, sensitivity of a given receiver, and the like.

When both OTFS pilot symbols and OTFS data symbols are transmittedaccording to the same transmitter OTFS time and frequency grid (102 g),and according to the same basis waveform (e.g. wherein the OTFS pilotbasis waveform W_(p) and the OTFS data basis waveform W_(d) are chosento be the same basis waveform), the topology or arrangement of whichgrid coordinates are used for OTFS pilot symbols, and which gridcoordinates are used for OTFS data symbols, can vary. Although in FIG.1B, the OTFS pilot symbols (120) were shown occupying a different(adjacent) portion of the transmitter OFTS grid (102 g) from the OTFSdata symbols (130), this need not always be the case.

In some embodiments, the grid time-frequency coordinates (td, tf) usedto transmit the OTFS data symbol waveform bursts can be chosen to eithersurround or to be adjacent to the time-frequency coordinates (pt, pf)used to transmit the OTFS pilot symbol waveform burst. In FIGS. 1B, 1C,1D, 2B, 2C, 3B, 3C and 4, the OTFS pilot symbols are adjacent to theOTFS data symbols. By contrast in FIG. 5, the OTFS pilot symbols areshown in a different topological configuration, where they aresurrounded, at least in part, by the OTFS data symbols.

FIG. 5 shows an embodiment where the OTFS pilot symbols (here the “1”and zeros) and OTFD data symbols (here a . . . p) are again on the sameOTFS time-frequency transmitter OTFS grid (102 g), but where the OTFSpilot symbol region (520) is embedded within the region of the gridotherwise used to transmit OTFD data symbols (530). Note that inaddition to the OTFS pilot symbols and data symbols, another OTFSsymbol, such as an OTFS checksum symbol (CS) (510), is also shown.

Note that in this scheme, although the underlying N×N matrix (here 4×4)OTFS data transmit matrix (540) used as an intermediate step in the OTFSdata transmission process may be a square matrix, the OTFS data symbolsused in the OTFS data transmit matrix may in some embodiments be furtherarranged or mapped by the OTFS transmitter processor (102 p) and memory(102 m) into other grid locations along the transmitter OTFS grid (102g). Here, as long as the receiver (104) is aware of this mapping, thereceiver can perform the inverse of this mapping after the other stepsof data channel deconvolution is done, recover a replica of the originalOTFS data transmit matrix, and then solve for the data bits using thepreviously described OTFS methods.

Note that as previously discussed, although wireless methods andwireless data channels are used as specific examples, these OTFS pilotmethods may be applied to a variety of different types of data channels.These data channels can include data channels (impaired data channels)such as optical fiber data channels comprising at least one opticalfiber (here the waveforms will typically be optical or infraredwaveforms), electrically conducting wire data channels comprising atleast one metallic electrical conductor (here the waveforms will beelectrical impulses or RF waveforms), or even data channels comprising afluid such as water (here the waveforms may be acoustic waveforms).

Wireless Embodiments

Going forward, the discussion here will more specifically focus onwireless data transmission methods.

In these wireless embodiments, the impaired data channel is a wirelessdata channel, the transmitter(s) and receivers are wirelesstransmitter(s) and receivers capable of movement (velocity) in space,and hence are subject to Doppler frequency shifts. That is, eachtransmitter has a transmitter velocity, and that transmitter's frequencyis at least partially determined by a transmitter Doppler shift thatvaries according to this transmitter velocity. Similarly each receiverhas a receiver velocity, and this receiver frequency is at leastpartially determined by a receiver Doppler shift that varies accordingto that receiver velocity.

In the wireless embodiment, the reflector(s) (106) reflect wirelesssignals (waveforms) and are also capable of movement in space (velocity)(108). Thus here, the reflector frequency shift(s) are receiver velocityDoppler shift(s). The various reflectors can be further characterized byvarious parameters. Thus here, for example, the at least one reflectorcoefficient of reflection is a reflector coefficient of wirelessreflection.

Thus in the wireless embodiment, the direct OTFS pilot bursts comprise aplurality of wireless OTFS pilot symbol waveform bursts. In the wirelessembodiment, the 2D channel state comprises information pertaining torelative locations, velocities, velocity induced frequency shifts causedby transmitter Doppler shifts, receiver Doppler shifts, reflectorDoppler shifts, and reflector coefficients of reflection of the varioustransmitters, receivers, and reflectors.

Despite these changes, the previous techniques, methods, and systems ofcharacterizing the data channel and determining the 2D channel statestill apply. However the wireless embodiments also enable furtherrefinements to the previously discussed techniques as well.

With regards to wireless transmission of data, the previously describedOTFS pilot burst techniques and 2D channel state acquisition techniquescan be useful for helping to improve wireless data sent by either legacy(e.g. prior art) methods, as well as useful for helping to improvewireless data sent by more advanced OTFS data transmission methods,which will be described shortly.

Thus for example, the methods described herein can be used by at leastone wireless transmitter, and at least one processor (often 102 p and104 p) to also (in addition to OTFS pilot bursts) transmit a pluralityof data symbols through the impaired data channel to at least onereceiver. Here the transmitter(s) (e.g. 102) will transmit at least someof the plurality of data symbols as direct data bursts. These directdata bursts comprise wireless data carrying waveform bursts. Here thedata symbols and wireless data carrying waveform bursts can betransmitted by various legacy (prior art) and non-legacy (e.g. OTFS)schemes, including Time division multiple access (TDMA), Global systemfor mobile communications (GSM), Frequency division multiple access(FDMA), Orthogonal frequency-division multiplexing (OFDM), Code divisionmultiple access (CDMA), OTFS wireless waveform bursts, or other types ofwireless waveform bursts. Thus unless otherwise specified use of OTFSwireless waveform bursts for data communications is not intended to belimiting for many of the claims.

As generally described previously in this disclosure, just as per theOTFS pilot bursts, the direct data bursts are also reflected off of thevarious wireless reflectors (e.g. 106), thereby producing replica databursts comprising direct data bursts that are further reflectortime-delayed and reflector velocity Doppler-shifted at the at least onewireless receiver (104). As before, at the various wireless receivers,the resulting combination of any transmitter Doppler-shifted andreceiver Doppler-shifted direct data bursts, and replica data bursts,produce channel-convoluted data bursts.

Again as previously described, the invention's methods can use the 2Dchannel state and at least one processor (often at least a receiverprocessor 104 p and associated memory 104 m), to deconvolute at leastsome of the channel-convoluted data bursts at the wireless receiver(s),thereby deriving at least an approximation of the originally transmittedplurality of data symbols. Alternatively or additionally, thereceiver(s) can also transmit 2D channel state derived commands, orother information pertaining to the 2D channel state, back to thetransmitter. The transmitter, often using at least one transmitterprocessor (102 p) and associated memory (102 m), can then optionally usethese commands to precode at least some of the direct data bursts topre-compensate for the effects of the impaired data channel.

In contrast to OTFS methods, which typically spread every data bit overa two dimensional time and frequency axis, many legacy wirelesswaveforms operate by spreading data over only a one-dimensional axis(e.g. only spread by time, only spread by frequency).

The 2D channel state information encompasses both types (time-frequency)of signal spreading, but tends to simultaneously report on how theimpaired data channel spreads signals over both time and frequency atthe same time. Thus, in some embodiments, if it is desired to transmitdata according to a non-OTFS legacy or prior art format, it may beuseful to further simplify the 2D channel state information to enable itto be more readily applied to help improve the transmission of suchlegacy wireless waveforms.

Such simplification can be done by, for example, using a 1D (onedimensional) projection of the 2D channel state information along any ofa time axis, frequency axis, or time-frequency axis. This projectionhelp convert the more sophisticated 2D channel state information into asimpler form that can then be applied to help either deconvolute orprecode legacy wireless waveform transmitted data.

Polarization Methods

In some embodiments, it can be useful to further use polarized OTFSpilot (wireless waveform) bursts to further characterize the datachannel impairments, and produce even more accurate 2D channel stateinformation. These methods take advantage of the fact that differenttypes of reflectors interact with polarized wireless waveforms indifferent ways. These differences can be exploited to help the systembetter distinguish between the various types of reflectors that arepresent in the data channel. Polarization methods are shown in moredetail in FIGS. 2A through 2C.

Here for example, at least one wireless transmitter (202) can beconfigured to transmit polarized wireless waveforms, for example usingpolarized antennas according to two polarization directions, such ashorizontally (202 h) and vertically (202 v). This transmitter (202)transmits direct OTFS pilot bursts as polarized direct OTFS pilot bursts(212 h) and (212 v). These direct OTFS pilot bursts comprise polarizedwireless OTFS pilot symbol waveform bursts that have been polarizedaccording to at least one polarization direction (here two differentdirections are shown). Here we will use linear polarization as aspecific example, but this example is not intended to be limiting, andother types of polarization (e.g. circular polarization, etc.) may alsobe used. Further assume that going forward the various transmitters andreceivers being discussed all have their own circuitry, processors, andmemory as previously discussed in FIG. 1B.

In this example, assume that at least one of the various wirelessreflector(s) in the data channel are polarization altering wirelessreflectors that alter the polarization direction of its reflectedwireless OTFS waveform bursts according to a first reflectorpolarization operator (e.g. polarization rotation angle, filter, tensor,etc.). As a result, such reflectors produce replica polarized OTFS pilotbursts that comprise polarization shifted time-delayed and reflectorDoppler-shifted replicas of the original polarized direct OTFS pilotbursts. Here, the wireless receiver(s) (204) should themselves befurther configured (usually with polarized antennas and suitablereceiver circuitry) to be able to detect a direction of polarization inthe received wireless waveforms. This can be done by using receiverantennas (usually a plurality of receiver antennas) configured to detectdifferent directions of polarization.

FIG. 2A shows how polarized OTFS pilot symbol waveform bursts can beused to further distinguish between different types of reflectors in theimpaired data channel. Here there are two reflectors (206), (208). Inthis admittedly contrived example, reflector (206) is positioned to bemore distant from the transmitter (202) and receiver (204). Furtherassume here that reflector (206) is a stationary reflector that onlyreflects vertically polarized waveforms.

In this example, assume that reflector (208) is positioned closer to thetransmitter (202) and (204), and that reflector (208) is also movingrapidly closer with respect to both with velocity “v” (209). Assumefurther that reflector (208) shifts the direction of polarization forall reflected polarized waveforms by 45 degrees.

The receiver and transmitter each have a horizontal and vertical antenna(202 h, 204 v, 204 h, 204 v). The transmitter can be further configuredto transmit two different (but time and frequency synchronized) streamsof data, one stream for each antenna, according to two different timeand frequency synchronized OTFS transmitter grids (202 gh, 202 gv). Thereceiver can be further configured to receive (synchronized by time andfrequency) data according to each receiver antenna polarizationdirection into two different time and frequency synchronized receiverbin structures (204 bh, 204 bv).

Thus, even in this simplified example, we end up with a complicated mixof direct bursts (212 h), (212 v), and replica bursts. These replicabursts include (214 ha) and (214 va) hitting reflector (206), whichabsorbs all of (214 va) and only reflects (214 hb) to the receiver(204), where only vertical polarized receiver antenna (204 h) can detectit. The replica bursts also include (216 ha) and (216 va) which travelto moving reflector (208). There, the moving reflector alters thedirection of both bursts by 45 degrees, and also imparts a Doppler shiftto both bursts, and thus each polarized receiver antenna (204 h) and(204 b) detects both frequency shifted and polarization shifted waveformbursts as a mixture of (216 vb) and (216 hb).

Due to the relative position of reflectors (206) and (208) in thisexample, assume that the time of arrival of the various bursts at thereceiver (204) is as follows. Because reflector (208) does not impartmuch additional distance to the signals, direct signals (212 h) and (212v) and replica signals (216 vb) (216 hb) arrive at both antennas (204 h)and (204 b) at about the same time. However because of the longerdistance traveled, signal (214 hb) arrives at receiver (214 h) at alater time.

Absent the invention's 2D channel state information, if the transmittertransmitted such different data streams, using the same time andfrequency slots, and same basic set of OTFS waveforms, the receiverwould have profound difficulties in distinguishing the two streams.However as will be discussed, due to polarization differences, by usingthe invention's 2D channel state information obtained from the OTFSpilot symbol waveforms, the receiver will be able distinguish betweenthe two data streams.

At the wireless receiver(s), the resulting combination of anytransmitter Doppler-shifted, receiver Doppler-shifted, and receiverpolarized direct OTFS pilot bursts and replica polarized OTFS pilotbursts produce channel-convoluted polarized OTFS pilot bursts. Thereceiver(s) can then receive these channel-convoluted polarized OTFSpilot bursts and detect their direction of polarization. The directionof polarization of these channel-convoluted polarized OTFS pilot burstscan then be used (often by one or more receiver processors) to furtherdetermine the 2D channel state of the impaired data channel.

FIG. 2B shows more details of the underlying transmitter grid structureand receiver bin structure regarding how the transmitter from FIG. 2Acan transmit different but time, frequency, and OTFS waveformsynchronized, streams of data from its horizontal and vertical antennas(202 h) and (202 v). Here assume that the transmitter's processor andmemory have stored two different OTFS grids (202 gh, and 202 gv) fortransmission. Here the transmitter's vertical polarized antenna (202 h)is transmitting pilot symbol “1” and OTFS data symbols “a, b, c, d, e,f, g, h, I” as various OTFS symbol waveform bursts according to the timeand frequency spacing shown in the OTFS transmitter grid (202 gv). Thetransmitter is also, at the exactly the same time, and exactly accordingto the same time and frequency spacing, using OTFS transmitter grid (202gh) to transmit pilot symbol “2” (time and frequency offset from pilotsymbol 1) and OTFS data symbols “j, k, l, m, n, o, p, q, r” on thehorizontal polarized antenna (204 h).

The various reflectors (206) (208) act on the various transmitted signalbursts as previously described in FIG. 2A. For illustrative purposes,the various time delays and frequency shifts are show producing arelatively large shift in the corresponding signal bursts as they arereceived according to the receiver's bin structure. The receiverreceives the channel convoluted OTFS waveform bursts on its polarizedantennas (204 v) and (204 h). Here the receiver reception on thereceiver's vertical polarized antenna (204 v) according to thereceiver's vertical polarized OTFS time-frequency bin structure (204 bv)is shown. Note how the 2D channel state has mixed the two streams upwith each other, but that the pilot symbol mixing pattern remainsrelatively easy for the receiver processor(s) to analyze.

In this diagram, to show that in some cases, the data channel mayproject the frequencies or times of an originally transmitted OTFSsignal burst relatively far into the frequencies or times normallyreserved for an adjacent OTFS signal burst (according to thetransmitter's grid structure) in some of the cases, multiple transmittedsignals are shown occupying the same receiver time-frequency bin. Notethat the size of the receiver bins in time and frequency typically willall be of constant size, but for these illustrations, in order to showmultiple signals showing up on the same bin, the bin size had drawnlarger to show all of the different signals and symbols.

Note also that at least when the data channel impairments cause a givenOTFS symbol to be projected on top of the time and frequency rangesimultaneously occupied by another OTFS symbol, as long as theunderlying OTFS waveforms used to transmit the different OTFS symbolsremain mutually orthogonal, then with the proper circuitry, the receivercan distinguish this mix and determine the different underlying OTFSsymbols.

FIG. 2C is very similar to FIG. 2B, except that here the eventshappening on the receiver's reception on the receiver's horizontalreceiver OTFS time-frequency bin (204 bh) structure is shown.

MIMO Methods

In some embodiments, it can be useful to further use multiple spatiallyseparated transmitting and receiving antennas to further characterizethe data channel impairments. Like polarization, but in a different way,MIMO methods also help both to produce more accurate 2D channel stateinformation, as well (as will be discussed) to help introduce anotherdimension of spatial separation to the data channel, which can beexploited to further increase the amount of data carried by the datachannel. MIMO methods are shown in more detail in FIGS. 3A through 3C.Note that these M IMO methods may be combined with the previouslydiscussed polarization methods to produce even higher levels of 2Dchannel state accuracy and overall system performance.

Before going further into MIMO discussions, it is useful to first expandon the concept of a “data stream”. Here an analogy to serial andparallel data transmission may be useful. It is known that data can betransmitted between transmitters and receivers according to serial andparallel data transmission schemes. Using wires as an analogy, when alldata bits travel over the same wire, this is generally understood to beserial communications. When different data bits are partitioned totravel over different wires, this is generally understood to be parallelcommunications.

Similarly in a wireless embodiment, although at first glance it mightlook as if the space over which wireless waveforms travel might be onlyone data channel, if the wireless waveforms are separated by differentfrequencies, or modulated by different (orthogonal to one another)waveforms, then a wireless analogy to parallel communications can alsoresult. As another example, if wireless communications are done betweendifferent sets of highly directional transmitter and receiver antennas,with minimal cross-talk between different sets of directionaltransmitter and receiver antennas, then each transmitter and receiverantenna set can be viewed as forming its own unique communicationschannel, and again parallel channels of communications can be achieved.

The distinction between serial and parallel starts to become blurredwhen multiple channels of wireless communication are transmitted at thesame time, same frequency, same underlying waveform, and using lessdirection specific (e.g. omnidirectional type antennas). However evenhere, just as at a cocktail party, human listener can, at least in someconditions, listen to various simultaneous conversations at the sametime and use two ears, sound echoes, and other types of audio channelcommunication impairments to in effect “tune in” to differentconversations at the same time.

As a simplified analogy, the invention's 2D channel state acquisitionmethods can also make use of clues obtained from various types of datachannel impairments to distinguish between different simultaneous“streams” of information.

How many different “streams” of information a data channel can supportcan be viewed as varying according to the underlying data channelstructure or impairments (e.g. distribution of reflectors) of the datachannel. Consider a case where the distribution of reflectors in a datachannel is such as to effectively create an isolated conduit betweeneach different transmitting antenna and each different receivingantenna. Such a data channel and 2D channel state could thus support alarge number of different streams of data in, limited mainly by thenumber of transmitting and receiving antennas.

By contrast, in a case where the data channel has no reflectors, and allof the transmitting and receiving antennas are omni-directional, then atleast with regards to transmitting different data symbols at the sametime, frequency, and underlying waveforms, problems caused byintersymbol-interference (isi) would greatly reduce the number ofdifferent streams that could be transmitted at the same time.

As previously discussed, the 2D channel state information can, in someembodiments, be represented by matrices, and with regards to differentstreams of information or data, the question of how many differentstreams can be simultaneously transmitted by a given data channel can beviewed (in linear algebra terms) somewhat in terms of the “rank” of the2D channel state matrix in this case. This rank is the size of thecollection of linearly independent rows (or columns, since column rankis equal to row rank) of the matrix. In some embodiments, this can alsobe viewed as the number of solutions of the system of linear equationsthat represent the effect of the impaired data channel on datatransmission.

The 2D channel state matrix can also be viewed as a scheme thatexpresses how waveforms input into the data channel by the transmitterare mutated by the data channel, and show up in the end as outputwaveforms detected by the receiver. In effect, to successfully transmitdifferent streams of data, not only must different streams of data beoriginally transmitted by the transmitter, but also at the end, thereceiver needs to be able to successfully separate (distinguish between)the different input streams of data as well.

Given this insight, the methods described herein thus teach that usingtechniques to improve the “rank” of the 2D channel state matrix, such asby using polarization and MIMO, to thus create higher rank 2D channelstate matrixes and “richer” data channels. These in turn allow wirelesssystems to operate at increasingly higher levels of performance (e.g.higher data transmission rates, lower energy per symbol, increasedresistance to fading, and the like). In some embodiments, improvement ofan order of magnitude and more over prior art methods may be achievedaccording to these schemes.

Put in simpler terms, the methods describe herein allow thecommunications system to quickly characterize the channel state of thewireless data channel, and determine if, for example, at any givenmoment there is a fortunate combination of reflectors that can enablethe data channel to send more streams of data than might otherwise bethe case. If so the invention's automated methods can take advantage ofthis fortunate combination of reflectors (some may be moving, some maybe stationary), and at least temporarily boost the number of streams ofdata sent to take advantage of this fortunate and possibly verytransient situation. The invention's automated methods also allow thesystem, given a deep understanding of this possibly temporarycombination of reflectors, to understand how to decode these multiplestreams of data. By contrast, prior art methods, which are notconfigured to take advantage of fortunate and possibly temporary chancearrangement of reflectors, operate comparatively inefficiently, relativeto what the inventions' methods show are now possible.

Note that although going forward this disclosure will thus focus on theinvention's particularly novel stream techniques, where signals are sentat the same times, frequencies, and underlying waveform types, thisteaching by no means disclaims other and more standard methods ofachieving parallelism, such as by transmitting at different times,different frequencies, and different underlying waveform types. Thusstandard methods of achieving parallel methods of data transmission mayalso be used in conjunction with the multiple stream methods disclosedherein.

Thus in some embodiments, particularly with regards to MIMO techniques,in addition to 2D channel state characterization, the system will alsotransmit direct data bursts as direct OTFS data bursts comprising OTFSdata symbols transmitted by OTFS wireless data symbol waveform bursts.Here in this MIMO configuration, on a per transmitter-receiver basis,the wireless transmitter may have T uniquely configured transmittingantennas, and the wireless receiver may R uniquely configured receivingantennas. Because this is MIMO, both T and R will be greater than 1, andR (the number of receiver antennas) may often be greater than or equalto T.

Here the wireless transmitter will be configured to use its Ttransmitting antennas to simultaneously transmit, over a same frequencyrange, at most T streams of stream identifiable direct OTFS data andpilot bursts. Here each stream identifiable direct OTFS data and pilotbursts will preferably have at least their various OTFS pilot symbolsP_(s,pt,pf) further chosen to be stream identifiable. In the examplesshown in FIGS. 3A-3C, for example, the first stream has a first OTFSpilot burst occupying a first OTFS transmitter OTFS grid location, whilethe second stream has a second OTFS pilot burst occupying a second OTFStransmitter OTFS grid location. As will be seen, these differences helpthe receiver determine the 2D channel state for each stream, and alsohelp deconvolute or correct for distortions caused by the impaired datachannel.

FIG. 3A shows how the system may also use spatially separatedtransmitting and receiving antennas (302 a 1, 302 a 2) and various OTFSpilot symbol waveform bursts to both further characterize the 2D channelstate of the data channel, and for other purposes as well. These otherpurposes can include imparting a spatial directionality to thetransmitted or receiving wireless waveforms, and also successfullytransmitting and receiving more streams of data at the same time,frequency, and OTFS wireless waveforms then would normally be possibleif the data channel had no impairments.

In particular, FIG. 3A shows a simplified MIMO situation where the MIMOtransmitter (302) has two spatially separated antennas, the MIMOreceiver (304) has two spatially separated antennas (304 a 1, 304 a 2),and there is one stationary reflector in the data channel (306), hereshown positioned closer to the left hand side of the transmitting andreceiving antennas than it is to the right hand side of the antennas.

Here, assume that the order of arrival of the various OTFS pilot bursts(and any data bursts as well) to the various receiving antennas is, withrespect to receiving antenna 304 a 1, first direct (312 a 1), thendirect (313 a 2), then replica (reflected) (314 a 1 to 314 ba 1), andfinally replica (reflected (314 a 2 to 314 ba 2). The different ordersof arrival can show up as different arrival times on the receiver binstructure (drawn this way in FIGS. 3B and 3C because this is easier toshow), or also as different waveform phases or different angles ofarrival on a higher dimensional representation of the receiver binstructure (not shown).

The order of arrival of the various OTFS pilot bursts is, with respectto receiving antenna (304 a 2), first (312 a 2), then (313 a 1), then(with a greater delay) replica (reflected (314 a 1 to 315 ba 1), andlast (due to the longer distance) replica (reflected) (314 a 2 to 315 ba2). Again the different orders of arrival can show up as differentarrival times on the receiver bin structure (drawn this way in FIGS. 3Band 3C here because this is easier to show), or also as differentwaveform phases or different angles of arrival on a higher dimensionalrepresentation of the receiver bin structure (not shown).

FIG. 3B shows how the MIMO transmitter from FIG. 3A can transmitdifferent but time, frequency, and OTFS waveform synchronized, streamsof data as different transmitter grids (302 g 1) (302 g 2 from its twoantennas (302 a 1 and 302 a 2). Here the MIMO transmitter's left antenna(302 a 1) is transmitting pilot symbol “1” and OTFS data symbols “a, b,c, d, e, f, g, h, I” as various OTFS symbol waveform bursts according tothe time and frequency spacing shown in the OTFS transmitter grid (302 g1). The MIMO transmitter is also, at the exactly the same time, andexactly according to the same time and frequency spacing, transmittingpilot symbol “2” (time and frequency offset from pilot symbol 1) andOTFS data symbols “j, k, l, m, n, o, p, q, r” on its left antenna (302 a2) according to grid (302 g 2). The reflector (306) acts on thesesignals as previously discussed in FIG. 3A. As previously discussed, dueto the spatial arrangement of the various antennas, the OTFS waveformsdo not all arrive simultaneously and at the same angle, but ratherarrive at different times (and different waveform phases, which alsovary as a function of time) and different angles.

To simplify the drawing, assume that the MIMO receiver antennas (304 a1) and (304 a 2) are receiving and detecting the slightly differenttravel times for the various transmitter antenna, reflector, andreceiver antenna configuration as different delay times on the receiverOTFS time-frequency bin structure. In actuality, the MIMO receiver mayoften instead detect these differences as differences in the phaseangles of the various waveforms, or even as different directions ofarrival of the various waveforms, and handle this using receiver binswith additional dimensions, but it is easier to show these differencesas time differences to illustrate the concept.

The MIMO receiver (304) receives the channel convoluted OTFS waveformbursts on its antennas. Here the MIMO receiver reception on the MIMOreceiver's left antenna (304 a 1) OTFS time-frequency bin structure (304b 1) is shown. Note how the 2D channel state has mixed the two streamsup with each other, but that the pilot symbol mixing pattern remainsrelatively easy for the receiver processor to analyze.

FIG. 3C is essentially a repeat of FIG. 3B, except that here the signalsreceived by the MIMO receiver's right hand antenna (304 a 2) accordingto this antenna's OTFS time-frequency bin structure (304 b 2) are shown.

As before, at the at least one wireless receiver antenna R_(a), aresulting combination of the transmitter Doppler-shifted and receiverDoppler-shifted stream identifiable direct OTFS data and pilot bursts,and replica stream identifiable direct OTFS data and pilot bursts,produce receiving antenna specific channel-convoluted streamidentifiable OTFS data and pilot bursts.

According to the invention's techniques, the T transmitting antennas andR receiving antennas should be configured so that the R receivingantennas receive different receiving antenna specific channel-convolutedstream identifiable OTFS data and pilot bursts with detectably different2D channel states. This can be done by various methods, including asufficiently large separation between the antennas, to impart an abilityfor the receiving antennas to sense the directionality of the incomingwireless waveforms, and/or configuring the receiver so that it furtherkeeps track of the relative phases of the incoming wireless waveforms.Here such phase detection methods can be particularly useful.

According to the invention's methods, the efficiency or chances ofsuccessfully transmitting the (at most) T streams of data to thewireless receiver using the receiver's R receiving antennas to receivethe antenna specific channel-convoluted stream identifiable OTFS dataand pilot bursts. Then, for each wireless receiving antenna R and eachstream identifiable plurality of OTFS pilot symbol waveforms, using aprocessor (typically a receiver processor) to determine the 2D channelstate at that that receiving antenna, thereby determining various streamspecific 2D channel states. These stream specific 2D channel states(e.g. the information in the stream specific 2D channel states) canthen, for example be used (often by the receiver processor) todeconvolute at least some of the antenna specific channel-convolutedstream identifiable OTFS data and pilot bursts at the receiver. Thisallows the receiver to therefore determine least an approximation of theoriginally sent, stream identifiable, data symbols.

Alternatively or additionally, as before, commands derived from this 2Dchannel state information, or some or all of the 2D channel stateinformation itself, can be sent to the transmitter. There, thetransmitter processor can use these commands or 2D channel stateinformation to precode at least some of this stream identifiable directOTFS data and pilot bursts to again pre-compensate for the impaired datachannel (or put alternatively, better exploit fortuitous reflectorarrangements in the impaired data channel for higher advantage).

More specifically, for situations such as this MIMO example, determiningor acquiring the 2D channel state in this situation can be done by usingat least one 2D impulse response to mathematically describe how the datachannel impairments cause various streams to be projected onto eachother. For example (using a two stream example of stream identifiabledirect OTFS data and pilot bursts) assume that stream-1 OTFS pilotsymbol waveform bursts P_(s1,t1,f1)·Wp(t1,f1) transmitted at a firsttime-frequency coordinate are projected by the data channel ontodifferent stream-2 OTFS pilot symbol waveform burstsP_(s2,t2,f2)·Wp(t2,f2) originally transmitted at a differenttime-frequency coordinate. The receiver detects this projection becausethe projected OTFS pilot symbol waveform end up being received intoreceiver bins that are different from those normally corresponding tothe stream-1 OTFS pilot symbol waveform bursts P_(s1,t1,f1)·Wp(t1,f1).This projection and resulting arrival into different receiver bins willvary according to a receiving antenna specific aspect of the impaireddata channel. Thus (if properly configured) the receiver will determine,for each different stream, R receiving antenna specific 2D impulseresponses. The receiver (often using the receiver processor) can thenuse, for each different stream, these R receiving antenna specific 2Dimpulse responses to deconvolute the receiving antenna specificchannel-convoluted stream identifiable OTFS data and pilot bursts.Alternatively or additionally, the receiver can transmit commands basedon these R-receiving antenna specific 2D impulse responses, or some orall of the 2D impulse response data, to the transmitter and thetransmitter can then use this information to further precode subsequenttransmitted streams as desired.

FIG. 4 shows an example of how after the MIMO receiver receives the twotransmitted streams according to the various OTFS bin structure (304 b1, 304 b 2) on its right and left hand antennas (304 a 1, 304 a 2), thereceiver processor can use the distribution of the known pilot symbolsto compute the 2D channel state of the impaired data channel. Thereceiver processor can, for example, describe this 2D channel state as a2D z-transform or other 2D transform, apply an inverse transform, andessentially deconvolute the channel convoluted OTFS pilot symbols andOTFS data symbols to reconstruct a cleaned-up receiver bin replica (404b 1, 404 b 2) of the two streams of data originally transmitted by theMIMO transmitter. (Because the receiver's bin structure will often behigher resolution than the original transmitter grid, some mapping backto the original OTFS grid structure can then be done by the receiverprocessor)

Again, the invention's method essentially turns a nominal liability—datachannel impairments, into an advantage because these impairmentsessentially provide a decoding key to help the receiver processorunscramble or deconvolute different data streams that otherwise mightnot be separable. In essence, the invention exploits data channelimpairments to in effect increase the maximum data carrying capacity ofthe data channel.

Again, note that these at most T different streams may be carried bycommonly shared OTFS carrier waveforms over the same ranges of times andfrequencies. Indeed, this is part of the definition of “stream”. Notethat of course this does not disclaim the possibility of also using theT antennas to transmit wireless data by different schemes, such asdifferent times, frequencies, OTFS carrier waveforms, and the like.

In some embodiments, the stream identifiable direct OTFS data and pilotbursts are also antenna identifiable and antenna specific. Here eachtransmitting antenna transmits an antenna specific stream of wirelessOTFS data symbol waveforms along with a plurality of antenna specificidentifiable wireless OTFS pilot symbol waveforms. However this is not arequirement. Indeed in other embodiments, which indeed may even bepreferred embodiments, this scheme may be dropped and insteadalternative schemes, which will be discussed shortly, may instead beadopted.

Methods Using a Combination of Polarization and MIMO Techniques

As previously discussed, in some embodiments, both polarization and MIMOtechniques may be combined to produce still higher levels ofperformance. Here, for example, at least some of the previouslydescribed T uniquely configured transmitting antennas can also beconfigured as differently polarized transmitting antennas. In thisconfiguration, the transmitter will further transmit its streamidentifiable direct OTFS data and pilot bursts as polarized streamidentifiable direct OTFS data and pilot bursts. These will betransmitted by the differently polarized transmitting antennas accordingto the different antenna polarization directions.

In this embodiment, as before, assume that at least one of the wirelessreflectors are polarization altering wireless reflectors that alters apolarization direction of its reflected wireless OTFS waveform burstsaccording to a first reflector polarization operator. Thus thisreflector produces polarized stream identifiable replica OTFS data andpilot bursts comprising polarization shifted time-delayed and reflectorDoppler-shifted replicas of the original polarized stream identifiabledirect OTFS data and pilot bursts.

In this embodiment, the receiver should have at least some of its Runiquely configured receiving antennas configured to detect a directionof polarization in the received wireless waveforms. As a result, at thewireless receiver, a resulting combination of any transmitterDoppler-shifted and receiver Doppler-shifted polarized streamidentifiable direct OTFS data and pilot bursts, and polarized streamidentifiable replica OTFS data and pilot bursts, will produce antennaspecific channel-convoluted stream identifiable polarized OTFS data andpilot bursts.

According to the invention's techniques, the receiver uses at least someof the receiver's R uniquely configured receiving antennas to receiveand detect the direction of polarization of these antenna specificchannel-convoluted stream identifiable polarized OTFS data and pilotbursts. Generally for each wireless receiving antenna R_(a) used in thisprocess, and each stream identifiable plurality of OTFS pilot symbolwaveforms, the receiver's processor can then analyze signals captured inthe receiver's bins, and use the receiver processor to then determinethe 2D channel state as seen at each receiving antenna R_(a) being used.This 2D channel state information can then be used, as before, todeconvolute at least some of the antenna specific channel-convolutedstream identifiable polarized OTFS data and pilot bursts, therebyderiving at least an approximation of the originally transmittedplurality of data symbols. Alternatively or additionally, commandsderived from the 2D channel state information, or some or all of the 2Dchannel state information, can be sent to the transmitter and used toprecode at least some of the polarized stream identifiable direct OTFSdata and pilot bursts to pre-compensate for the impaired data channel.

Transmitter Precoding Methods

As previously discussed, MIMO applications where multiple transmittingantennas are used to shape a spatial directionality of the transmittedwireless beam (e.g. select what directions will get peaks and nulls ofthe transmitted wireless waveforms) are well known in the art. SimilarlyMIMO applications where multiple receiving antennas are used to shape aspatial directionality in receiver sensitivity (e.g. select whatdirections will get enhanced sensitivity [peaks] and what directionswill tend get diminished sensitivity [nulls] are well known in the art.Often such beam forming can be done using the previously discussed phaseangle adjustment methods.

Such methods are not disclaimed here. Indeed in some embodiments, thepreviously discussed 2D channel state and precoding methods may befurther used to shape a spatial directionality of the wireless waveformstransmitted by the T uniquely configured transmitting antennas.Alternatively or additionally, the 2D channel state information andpreviously discussed 2D channel state assisted deconvolution methods mayalso be used to shape a spatial directionality of the wireless waveformsreceived by the R uniquely configured receiving antennas.

As one example, this spatial directionality may be achieved by using thetransmitter processor to adjust any of relative phases or angles of thewireless waveforms transmitted by the T uniquely configured transmittingantennas. Alternatively or additionally, the spatial directionality ofthe wireless waveforms received by the R uniquely configured receivingantennas may be achieved by using the receiver processor to monitor therelative phases or angles of the wireless waveforms received by the Runiquely configured receiving antennas.

Advanced Transmitter Precoding Methods

In some embodiments, where the system attempts to exploit the underlyingstructure of the data channel (e.g. position of various reflectors,other channel imperfections) to transmit more than one stream of data atthe same time, it may also be desired to also use the multipletransmitting and receiving antennas to control the directionality of thewireless antenna beam (either at the transmitting or receiving end).

Here, it still will be useful to transmit stream identifiable OTFS dataand pilot bursts, but if it is desired to use multiple antennas tocontrol the directionality of the beam, in a preferred embodiment, itmay not be desirable to transmit transmitting antenna identifiablesignals. Instead, the transmitter processor may transmit the same streamidentifiable OTFS data and pilot bursts through more than one antenna atthe same time, in some embodiments with a varying phase delay oradjustment between the different antennas, thus providingdirectionality. The same principle can also be used by the receiver aswell.

In these embodiments of the invention, the transmitter does notconfigure the stream identifiable direct OTFS data and pilot bursts tobe antenna identifiable and or antenna specific. Instead, each differenttransmitting antenna may transmit at least one stream (e.g. often morethan one stream) of wireless OTFS data symbol waveforms along the atleast one stream identifiable wireless OTFS pilot symbol waveforms.

For example, in such embodiments, each transmitting antenna maytransmits at least one stream of wireless OTFS data symbol waveformsalong with at least one stream identifiable wireless OTFS pilot symbolwaveforms according to various transmitting antenna specific phases orpower settings. This in effect thereby shapes a spatial directionalityto the wireless waveforms transmitted by those transmitting antennasthat are transmitting that particular stream.

Further Details of OTFS Waveform Structure and OTFS Burst Structure

In some embodiments, the OTFS waveforms bursts may be produced andstructured according to methods previously discussed in patentapplications U.S. 61/349,619, U.S. Ser. No. 13/177,119, U.S. Ser. Nos.13/430,690 and 13/927,091 as well as U.S. Pat. Nos. 8,547,988 and8,879,378; the complete contents of all of which are incorporated hereinby reference in their entirety. Some specific examples of some of theseembodiments are discussed below.

FIG. 6 shows an example of circuitry useful to implement an OTFStransmitter transmitting a series of N consecutive OTFS waveform bursts(previously called blocks in parent application Ser. No. 13/430,690). Insome embodiments, the transmitter may further incorporate apre-equalization step to pre-compensate for various communicationschannel impairments such as echo reflections and frequency shifts.

This transmitter can comprise a more digitally oriented computation end(e.g. previously discussed 102 p) (which may use a processor and memory)and a more analog signal oriented modulation end (previously discussed102 c). At the digital end (102 p), an electronic circuit, which may bea microprocessor, digital signal processor, or other similar device willaccept as input the data matrix [D] (603) and may either generate oraccept as inputs the [U₁] (604) (e.g. a DFT/IDFT matrix) and [U₂] (605)(e.g. the encoding matrix U as discussed elsewhere) matrices as well asthe permutation scheme P, previously described here and in parentapplication Ser. No. 13/117,119, again incorporated herein by reference,as well as in the example later on in the document. The digital sectionwill then generate what was referred to in '119 as the TFSSS matrix (andhere referred to as an OTFS matrix), and what can alternatively betermed the OTFS (time/frequency shift) matrix. Once generated,individual elements from this matrix may be selected, often by firstselecting one column of N elements from the OTFS matrix, and thenscanning down this column and picking out individual elements at a time(606). Generally one new element will be selected every time block.Other scanning schemes can also be used.

Thus every successive time slice, one element from the OTFS matrix (608)can be used to control the modulation circuit (102 c). In one embodimentof the invention, the modulation scheme will be one where the elementwill be separated into its real and imaginary components, chopped andfiltered, and then used to control the operation of a sin and cosinegenerator, producing a composite analog waveform (620). The net, effect,by the time that the entire original N×N data symbol matrix [D] istransmitted, is to transmit the data in the form of N²summation-symbol-weighted cyclically time shifted and cyclicallyfrequency shifted waveforms, structured as N composite waveform bursts.In the example shown in FIG. 6, the data is transmitted over Nconsecutive waveform bursts over N time blocks. However as discussedelsewhere, other schemes are also possible, such as schemes in whichsome of composite waveforms are transposed to a different frequencyrange, and transmitted in parallel at the same time. In general thecomposite waveforms may be transmitted over any combination of N timeblocks or frequency blocks.

In some embodiments, at the transmitter end, a microprocessor controlledtransmitter may package a series of different symbols “d” (e.g. d₁, d₂,d₃ . . . ) for transmission by repackaging or distributing the symbolsinto various elements of various N·N matrices [D] by, for exampleassigning d₁ to the first row and first column of the [D] matrix (e.g.d₁=d_(0,0)), d₂ to the first row second column of the [D] matrix (e.g.d₂=d_(0,1)) and so on until all N·N symbols of the [D] matrix are full.Here, once we run out of d symbols to transmit, the remaining [D] matrixelements can be set to be 0 or other value indicative of a null entry.

The various primary waveforms used as the primary basis for transmittingdata, which here will be called “tones” to show that these waveformshave a characteristic sinusoid shape, can in some embodiments bedescribed by an N·N Inverse Discrete Fourier Transform (IDFT) matrix[W], where for each element w in [W],

$w_{j,k} = e^{\frac{i\; 2\pi\; j\; k}{N}}$or alternatively w_(j,k)=e^(ijθ) ^(k) or w_(j,k)=[e^(iθ) ^(k) ]^(j).Thus the individual data elements d in [D] are transformed anddistributed as a combination of various fundamental tones w by schemessuch as a matrix multiplication operation [W]*[D], producing a tonetransformed and distributed form of the data matrix, here described bythe N·N matrix [A], where [A]=[W]*[D].

To produce the invention's N cyclically time shifted and N cyclicallyfrequency shifted waveforms, the tone transformed and distributed datamatrix [A] may then itself be further permuted, for example usingmodular arithmetic or “clock” arithmetic, creating an N·N matrix [B],where for each element of b of [B], b_(i,j)=a_(i,(i+j)mod N). This canalternatively be expressed as [B]=Permute([A])=P(IDFT*[D]). Thus in someembodiments, this clock arithmetic can control the pattern of cyclictime and frequency shifts.

In some embodiments, a unitary matrix [U] can then be used to operate on[B], producing an N·N transmit matrix [T], where [T]=[U]*[B], thusproducing a N² sized set of all permutations of N cyclically timeshifted and N cyclically frequency shifted waveforms determinedaccording to an encoding matrix [U]. Put alternatively, in theseembodiments, the N·N transmit matrix [T]=[U]*P(IDFT*[D]). This N·Ntransmit matrix can be viewed as corresponding to the previouslydiscussed transmitter OTFS time-frequency grid.

In these embodiments, often on a per column basis, each individualcolumn of N can be used by the transmitter processor and transmitter tofurther modulate a frequency carrier wave (e.g. if we are transmittingin a range of frequencies around 1 GHz, the carrier wave will be set at1 GHz), and each column the N·N matrix [T] which has N elements, maythus produce N symbol-weighted cyclically time shifted and cyclicallyfrequency shifted waveform bursts for each data symbol. In theseembodiments, the transmitter is transmitting the sum of the Nsymbol-weighted cyclically time shifted and cyclically frequency shiftedwaveforms from one column of [T] at a time as, for example, a compositewaveform over a time block of data, thus creating a waveform “burst”.

Alternatively the transmitter could instead use a different frequencycarrier wave for the different columns of [T], and thus for exampletransmit one column of [T] over one frequency carrier wave, andsimultaneously transmit a different column of [T] over a differentfrequency carrier wave, thus transmitting more data at the same time,although of course using more bandwidth to do so. This alternativemethod of using different frequency carrier waves to transmit more thanone column of [T] at the same time will be referred to as frequencyblocks, where each frequency carrier wave burst is considered its ownfrequency block.

Thus, in some embodiments, since the N·N matrix [T] has N columns, thetransmitter will transmit the N² summation-symbol-weighted cyclicallytime shifted and cyclically frequency shifted waveforms, structured as Ncomposite waveform bursts, over any combination of N time blocks orfrequency blocks.

FIG. 7 shows an example of circuitry (such as 104 c) useful to implementan OTFS receiver. As previously discussed, this receiver will normallybe controlled by a receiver processor (104 p) and associated memory sothat the receiver can simultaneously track incoming OTFS waveforms at aplurality of times and frequencies according to the previously describedOTFS receiver bin structure, as well as optionally also monitor any ofpolarization on multiple antennas, waveform phase on multiple antennas,or direction of incidence on multiple antennas, and send the results tothe receiver processor and memory for further analysis as discussedelsewhere in this specification.

On the receiver side, the transmit process is essentially reversed.Here, for example, a microprocessor controlled receiver would of coursereceive the various columns [T] (e.g. receive the N composite waveformbursts, also known as the N symbol-weighted cyclically time shifted andcyclically frequency shifted waveform bursts) (702) into the variousOTFS time-frequency receiver bins over various time blocks or frequencyblocks as desired for that particular application. If for example thereis a lot of available bandwidth and time is of the essence, then thetransmitter will transmit, and the receiver will receive, the data asmultiple frequency blocks over multiple frequency carrier waves. On theother hand, if available bandwidth is more limited, and/or time(latency) is less critical, then the transmit will transmit and thereceiver will receive over multiple time blocks instead.

Note that as previously discussed, the receiver bin structure may oftenbe finer (e.g. higher resolution) than the underlying OTFS N·Ntransmission or receiving matrix. According to the invention, thishigher resolution will typically be used for 2D channel statecharacterization, deconvoluting data channel impairments, and the like.Once the previously described 2D channel state methods are used to cleanup the received data according to the receiver bin structure, the datafrom the cleaned up receiver bins (704) can then be mapped (usuallyusing the receiver processor) into the N·N receive matrix [R], and theoriginal transmitted data extracted as discussed below.

So effectively the receiver tunes into the one or more frequency carrierwaves, and over the number of time and frequency blocks set for thatparticular application eventually receives the data or coefficients fromoriginal N·N transmitted matrix [T] as into the receiver bin structure,cleans up this data using the 2D channel effects, and then maps thecleaned up data into the N·N receive matrix [R] where [R] is similar to[T], but may not be identical due to various remaining communicationsimpairments.

In some embodiments, the microprocessor controlled receiver can thenreverse the transmit process by a series of steps that mimic, inreverse, the original transmission process. The N·N receive matrix [R]may first be decoded by inverse decoding matrix [U^(H)], producing anapproximate version of the original permutation matrix [B], here called[B^(R)], where [B^(R)]=([U^(H)]*[R]).

The receiver then, for example, can do an inverse clock operation toback out the data from the cyclically time shifted and cyclicallyfrequency shifted waveforms (or tones) by doing an inverse modularmathematics or inverse clock arithmetic operation on the elements of theN·N [B^(R)] matrix, producing, for each element b^(R) of the N·N [B^(R)]matrix, a_(i,j) ^(R)=b_(i,(j−i)mod N) ^(R). This produces a“de-cyclically time shifted and de-cyclically frequency shifted” versionof the tone transformed and distributed form of the data matrix [A],here called [A^(R)]. Put alternatively, [A^(R)]=Inverse Permute([B^(R)]), or [A^(R)]=P⁻¹[U^(H)]*[R]).

In some embodiments, the receiver processor (104 p) can then furtherextract at least an approximation of the original data symbols d fromthe [A^(R)] matrix by analyzing the [A] matrix using (for example) anN·N Discrete Fourier Transform matrix DFT of the original InverseFourier Transform matrix (IDFT).

Here, for each received symbol d^(R), the d^(R) are elements of the N·Nreceived data matrix [D^(R)] where [D^(R)]=DFT*A^(R), or alternatively[D^(R)]=DFT*P⁻¹([U^(H)]*[R]).

Thus the original N² summation-symbol-weighted cyclically time shiftedand cyclically frequency shifted waveforms are transmitted according tothe transmitter OTFS grid, along with OTFS pilot waveform bursts. Duringtransmission, all waveform bursts are subject to the various datachannel impairments as previously described. The receiver receives thevarious OTFS waveform bursts according to the receiver bin structure,and uses the OTFS pilot waveform bursts to determine the 2D channelstate of the data channel. The receiver can then use this 2D channelstate to further clean up (deconvolute) the received OTFS data bursts,and then map the deconvoluted OTFS data bursts back into the receiverN·N receive matrix [R].

Once this occurs, the receiver processor and memory can use acorresponding decoding matrix U^(H) (also represented as [U^(H)]) tocomplete the process of backing out the original data from the receivedOTFS symbols. Here the receiver (e.g. the receiver's microprocessor andassociated software) can use this decoding matrix [U^(H)] to reconstructthe various transmitted symbols “d” in the one or more originallytransmitted N·N symbol matrices [D] (or at least an approximation ofthese transmitted symbols).

The invention claimed is:
 1. A receiver apparatus, comprising: a memory,a processor; and a network interface; wherein the processor readsinstructions from the memory and implements an automated method ofacquiring a 2D channel state of an impaired data channel connecting atleast one transmitter and the receiver via the network interface, saidimpaired data channel comprising at least one reflector, each said atleast one reflector comprising a reflector location, reflector frequencyshift, and at least one reflector coefficients of reflection; thetransmitter comprising a transmitter location and transmitter frequencyshift; the receiver comprising a receiver location and receiverfrequency shift; wherein said 2D channel state comprises informationpertaining to relative locations, frequency shifts, and reflectorcoefficients of reflection of said transmitter, the receiver, andreflectors; wherein the transmitter transmits direct orthogonal timefrequency space (OTFS) pilot bursts, said direct OTFS pilot burstscomprising a plurality of OTFS pilot symbols P_(pt,pf) transmuted asOTFS pilot symbol waveform bursts P_(pt,pf)·W_(p)(pt, pf), over aplurality of combinations of times pt and frequencies pf, where eachsaid pt and pf are unique pilot time-frequency coordinates chosen from atwo dimensional pilot OTFS time-frequency grid, and all said OTFS pilotsymbol waveform bursts P_(pt,pf)·W_(p)(pt, pf) are mutually orthogonalwaveform bursts derived from cyclically time and frequency shiftedversions of a same OTFS pilot basis waveform W_(p); said instructionscomprising: instructions for receiving at least said pilot burstsaccording to at least a two dimensional pilot OTFS time-frequency binstructure with bin sizes and bin-coordinate positions proportional tosaid OTFS time-frequency grid; wherein upon propagation through saidimpaired data channel, said direct OTFS pilot bursts then travel over atleast one path, said at least one path comprising at least one of: a:direct OTFS pilot bursts traveling directly from said transmitter tosaid receiver; and b: replica OTFS pilot bursts comprising direct OTFSpilot bursts that have reflected off of said at least one reflectorbefore reaching said receiver, thereby producing direct OTFS waveformbursts that are further reflector time-delayed and reflectorfrequency-shifted at said receiver; wherein at said receiver, aresulting combination of any said transmitter frequency shifted andreceiver frequency shifted direct OTFS pilot bursts and any said replicaOTFS pilot bursts produces channel-convoluted OTFS pilot bursts; theinstructions further comprising: instructions for, at said at least onereceiver, using said bin structure to receive said channel-convolutedOTFS pilot bursts and to determine said 2D channel state of saidimpaired data channel connecting said transmitter and said receiver. 2.The receiver of claim 1, wherein prior to transmission, said pluralityof OTFS pilot symbols P_(pt,pf), and two dimensional pilot OTFStime-frequency grid and bin structure are chosen so that if, aftertransmission by said transmitter, said impaired data channelsubsequently causes at least some of said OTFS pilot symbol waveformbursts P_(t1,f1)W_(p)(t1, f1) originally transmitted at a firsttime-frequency coordinate to be projected onto different OTFS pilotsymbol waveform bursts P_(t2,f2)Wp(t2, f2) originally transmitted at adifferent time-frequency coordinate, and bins different from thosenominally corresponding to said OTFS pilot symbol waveform burstsP_(t1,f1)W_(p)(t1, f1), at least some of said projections will bedetectable and quantifiable by said receiver.
 3. The receiver of claim2, wherein said plurality of OTFS pilot symbols P_(pt,pf) transmitted asOTFS pilot symbol waveform bursts P_(pt,pf)W_(p)(pt, pf) comprise atleast one non-null OTFS pilot symbol P_(pt,pf) transmitted as an OTFSpilot symbol waveform burst P_(pt,pf)W_(p)(pt, pf) with sufficient powerto be detectable by said receiver; and any of: 1: at least some of saidplurality of OTFS pilot symbols are null pilot symbols intended tocreate empty pt and pf unique pilot time-frequency coordinates chosenfrom said two dimensional pilot OTFS time-frequency grid, where nowaveform burst is transmitted; or 2: at least some of said plurality ofOTFS pilot symbols are background pilot symbols intended to create auniform background of pt and pf unique pilot time-frequency coordinateschosen from said two dimensional pilot OTFS time-frequency grid toenable projections of channel-convoluted non-null OTFS pilot bursts ontosaid uniform background to be detectable and quantifiable by saidreceiver.
 4. The receiver of claim 1, wherein said 2D channel state isat least partially determined by using at least one 2D impulse responseto mathematically describe how said impaired data channel causes atleast some of said OTFS pilot symbol waveform bursts P_(t1,f1)W_(p)(t1,f1) transmitted at a first time-frequency coordinate to be projectedonto different OTFS pilot symbol waveform bursts P_(t2,f2) W_(p)(t2, f2)originally transmitted at a different time-frequency coordinate, andbins different from those nominally corresponding to said OTFS pilotsymbol waveform bursts P_(t1,f1)W_(p)(t1, f1).
 5. The receiver of claim4, further using a plurality of said 2D impulse responses from aplurality of said bins to at least partially describe said 2D channelstate as at least one 2D transform comprising at least one of a 2DZ-transform or other 2D transform.
 6. The receiver of claim 1, whereinsaid plurality of OTFS pilot symbols P_(pt,pf) are known by saidreceiver, and wherein said plurality of OTFS pilot symbols are furtherchosen to be any of: one or two dimensional m-sequences comprisingbinary maximal-length shift register sequences, delta values P_(i,j)surrounded by regions of P_(pt,pf) zero values, one or two dimensionalBarker codes, Costas arrays, Walsh matrixes, or other plurality of pilotsymbols selected to facilitate acquiring said 2D channel state; andwherein said bins have time-frequency resolutions that are equal to ormore precise than time-frequency resolutions of said grid.
 7. Thereceiver of claim 1, further receiving a plurality of data symbolsthrough said impaired data channel transmitted by said transmitter asdirect data bursts comprising a plurality of data carrying waveformbursts, and to receive said direct data bursts along with said directOTFS pilot bursts to said at least one receiver; wherein said directdata bursts also are reflected off of said at least one reflector,thereby producing replica data bursts comprising time-delayed andreflector frequency-shifted direct data bursts at said receiver, andwherein at said receiver, a resulting combination of any saidtransmitter frequency shifted and receiver frequency shifted direct databursts, and replica data bursts, produce channel-convoluted data bursts;wherein the instructions further include: instructions for using said 2Dchannel state to deconvoluting at least some of said channel-convoluteddata bursts at said at least one receiver, thereby deriving at least anapproximation of said plurality of data symbols.
 8. The receiver ofclaim 1, wherein said impaired data channel is an optical fiber datachannel comprising at least one optical fiber, an electricallyconducting wire data channel comprising at least one metallic electricalconductor, or a data channel comprising a fluid.
 9. The receiver ofclaim 1, wherein said impaired data channel is a wireless data channel,said transmitter is a wireless transmitter, said receiver is a wirelessreceiver, said reflector is a wireless reflector further comprising areflector velocity, said reflector frequency shift is a receivervelocity Doppler shift, and said at least one reflector coefficient ofreflection is a reflector coefficient of wireless reflection; saidtransmitter has a transmitter velocity, and said transmitter frequencyis at least partially determined by a transmitter Doppler shift thatvaries according to said transmitter velocity; said receiver has areceiver velocity, and said receiver frequency is at least partiallydetermined by a receiver Doppler shift that varies according to saidreceiver velocity; said direct OTFS pilot bursts comprise a plurality ofwireless OTFS pilot symbol waveform bursts; and wherein, said 2D channelstate comprises information pertaining to relative locations,velocities, velocity induced frequency shifts caused by transmitterDoppler shifts; receiver Doppler shifts, reflector Doppler shifts, andreflector coefficients of reflection of said at least one transmitters,receivers, and reflectors.
 10. The receiver of claim 9, wherein saiddirect data bursts also are reflected off of said at least one wirelessreflector, thereby producing replica data bursts comprising direct databursts that are further reflector time-delayed and reflector velocityDoppler-shifted at said at least one wireless receiver, and wherein atsaid receiver, a resulting combination of any said transmitterDoppler-shifted and receiver Doppler-shifted direct data bursts andreplica data bursts produce channel-convoluted data bursts; theinstructions further comprising: instructions for using said 2D channelstate to further b) deconvoluting at least some of saidchannel-convoluted data bursts at said at least one wireless receiver,thereby deriving at least an approximation of said plurality of datasymbols; wherein said data symbols and wireless data carrying waveformbursts conform to any of TDMA, GSM, FDMA, OFDM, CDMA, OTFS wirelesswaveform bursts, or other types of wireless waveform bursts.
 11. Thereceiver of claim 10, wherein said deconvoluting is done by using atleast one 1D projection of said 2D channel state along any of a timeaxis, frequency axis, or time-frequency axis.
 12. The receiver of claim10, wherein said direct OTFS pilot bursts include polarized direct OTFSpilot bursts comprising polarized wireless OTFS pilot symbol waveformbursts according to at least one polarization direction; said at leastone wireless reflector is a polarization altering wireless reflectorthat alters a polarization direction of its reflected wireless OTFSwaveform bursts according to a first reflector polarization operator,thereby producing replica polarized OTFS pilot bursts that comprisepolarization shifted time-delayed and reflector Doppler-shifted replicasof said polarized direct OTIS pilot bursts; said at least one wirelessreceiver is further configured to detect a direction of polarization inits received wireless waveforms; and wherein at said wireless receiver,a resulting combination of any said transmitter Doppler-shifted,receiver Doppler-shifted, and receiver polarized direct OTFS pilotbursts and replica polarized OTFS pilot bursts producechannel-convoluted polarized OTFS pilot bursts; the instructions furtherincluding: instructions for receiving said channel-convoluted polarizedOTFS pilot bursts and detecting their direction of polarization; andinstructions for further using said direction of polarization of saidchannel-convoluted polarized OTFS pilot bursts to further determine said2D channel state of said impaired data channel.
 13. The receiver ofclaim 10, wherein said direct data bursts are direct OTFS data burstscomprising OTFS data symbols transmitted by OTFS wireless data symbolwaveform bursts; said wireless receiver configured to simultaneouslyreceive, over a same frequency range, at most T streams of streamidentifiable direct OTFS data and pilot bursts, each stream identifiabledirect OTFS data and pilot bursts having at least OTFS pilot symbolsP_(s,pt,pf) further chosen to be stream identifiable; wherein saidwireless receiver has R uniquely configured receiving antennas, both Tand R being greater than 1, and R being greater than or equal to T;wherein at said at least one wireless receiver antenna R_(a), aresulting combination of any said transmitter Doppler-shifted andreceiver Doppler-shifted stream identifiable direct OTFS data and pilotbursts, and replica stream identifiable direct OTFS data and pilotbursts, produce receiving antenna specific channel-convoluted streamidentifiable OTFS data and pilot bursts; the instructions comprising:instructions for, for each wireless receiving antenna R and each streamidentifiable plurality of OTFS pilot symbol waveforms, determining said2D channel state at said receiving antenna, thereby determining streamspecific 2D channel states, and use said stream specific 2D channelstate for b) deconvoluting at least some of said antenna specificchannel-convoluted stream identifiable OTFS data and pilot bursts atsaid at least one receiver, thereby deriving at least an approximationof said plurality of data symbols.
 14. The receiver of claim 13, whereinthe instructions for determining said 2D channel state further include:instructions for using at least one 2D impulse response tomathematically describe how, for said stream identifiable direct OTFSdata and pilot bursts, stream-1 CATS pilot symbol waveform burstsP_(s1,t1,f1)Wp(t1,f1) transmitted at a first time-frequency coordinateto be projected onto different stream-2 OTFS pilot symbol waveformbursts P_(s2,t2,f2)Wp(t2,f2) originally transmitted at a differenttime-frequency coordinate, and bins different from those normallycorresponding to said stream 1 OTFS pilot symbol waveform burstsP_(s1,t1,f1)Wp(t1,f1), according to a receiving antenna specific aspectof said impaired data channel, thereby determining, for each stream, Rreceiving antenna specific 2D impulse responses; and instructions forusing said R receiving antenna specific 2D impulse responses to eitherprecode said streams at said transmitter, or deconvolute said receivingantenna specific channel-convoluted stream identifiable OTFS data andpilot bursts.
 15. The receiver of claim 13, wherein said at least onewireless reflector is a polarization altering wireless reflector thatalters a polarization direction of its reflected wireless OTFS waveformbursts according to a first reflector polarization operator, therebyproducing polarized stream identifiable replica OTFS data and pilotbursts comprising polarization shifted time-delayed and reflectorDoppler-shifted replicas of said polarized stream identifiable directOTFS data and pilot bursts; said receiver has at least some of its Runiquely configured receiving antennas configured to detect a directionof polarization in its received wireless waveforms; wherein at saidreceiver, a resulting combination of any said transmitterDoppler-shifted and receiver Doppler-shifted polarized streamidentifiable direct OTFS data and pilot bursts; and polarized streamidentifiable replica OTFS data and pilot bursts, produce antennaspecific channel-convoluted stream identifiable polarized OTFS data andpilot bursts; the instructions including: instructions for further usingat least some of said receiver's R uniquely configured receivingantennas to receive and detect the direction of polarization of saidantenna specific channel-convoluted stream identifiable polarized OTFSdata and pilot bursts; instructions for, for each wireless receivingantenna R_(a) and each stream identifiable plurality of OTFS pilotsymbol waveforms, determining said 2D channel state at said receivingantenna R_(a), and using said 2D channel states for deconvoluting atleast some of said antenna specific channel-convoluted streamidentifiable polarized OTFS data and pilot bursts at said at least onereceiver, thereby deriving at least an approximation of said pluralityof data symbols.
 16. The receiver of claim 13, wherein said 2D channelstate and said deconvoluting is used to shape a spatial directionalityof the wireless waveforms received by said R uniquely configuredreceiving antennas.
 17. The receiver of claim 16, wherein theinstructions further include: Instructions for achieving said spatialdirectionality of the wireless waveforms received by said R uniquelyconfigured receiving antennas by monitoring the relative phases orangles of the wireless waveforms received by said R uniquely configuredreceiving antennas.
 18. The receiver of claim 13, wherein said at most Tdifferent streams are carried by commonly shared OTFS carrier waveformsover a same ranges of times and frequencies.
 19. The receiver of claim13, wherein each said stream identifiable direct OTFS data and pilotbursts are not antenna identifiable and not antenna specific.
 20. Thereceiver of claim 13, wherein said stream identifiable direct OTFS dataand pilot bursts are antenna identifiable and antenna specific.